Geographically Weighted Visualization: Interactive Graphics for Scale-Varying Exploratory Analysis Abstract -We introduce a series of geographically weighted (GW) interactive graphics, or geowigs, and use them to explore spatial relationships at a range of scales. We visually encode information about geographic and statistical proximity and variation in novel ways through gw-choropleth maps, multivariate gw-boxplots, gw-shading and scalograms. The new graphic types reveal information about GW statistics at several scales concurrently. We impement these views in prototype software containing dynamic links and GW interactions that encourage exploration and refine them to consider directional geographies. An informal evaluation uses interactive GW techniques to consider Guerry's dataset of 'moral statistics', casting doubt on correlations originally proposed through visual analysis, revealing new local anomalies and suggesting multivariate geographic relationships. Few attempts at visually synthesising geography with multivariate statistical values at multiple scales have been reported. The geowigs proposed here provide informative representations of multivariate local variation, particularly when combined with interactions that coordinate views and result in gw-shading. We argue that they are widely applicable to area and point-based geographic data and provide a set of methods to support visual analysis using GW statistics through which the effects of geography can be explored at multiple scales. Definitions of geovisualization and information visualization suggest mutual exclusivity -yet in practice much geovisualization is dependent on and informed by aspatial graphics and many views that combine elements of geography and statistical spaces provide useful insights. The value added in combining these elements to help explain geographical processes is that exploring relationships between measured phenomena that are 'near' in statistical space and geographical space may provide insights that cannot be achieved with maps or statistical graphics alone. The definition of 'nearness' is fundamental to such approaches: How near do two houses have to be before the selling price of one influences the selling price of the other? How near does an area with a high crime rate have to be from a house to influence its selling price? Is the relationship a simple monotone or might there be more than one 'critical distance' at which interactions occur? And do these relationships vary across space and with direction? These kinds of questions consider geographical interaction between variables but also imply that an investigation of scale must be considered.. A popular approach to the investigation of geographical patterns is the concept of local statistics [11, 18] perhaps arising from Openshaw's stated dissatisfaction with 'whole map statistics' [15] . A point location u in a study area is selected, and some statistical technique applied to the data weighted by proximity to u. Applying this procedure to a number of locations spanning the study area gives an indication of the spatial variability in the distribution of the data values. Such approaches have incorporated not only formal inferential methods, such as the g-statistic [11] , or geographically weighted regression (GWR) [1] , but also descriptive tools, such as geographically weighted summary statistics [2] . The latter approach allows us to consider spatial patterns of attributes through localized descriptive statistics and is suitable for considering the geography of a statistical data set in the context of exploratory enquiry.. For the 'geographically weighted' approaches, the rate at which weighting reduces with distance is controlled by a parameter h: typically h is either a fixed distance for all u, or chosen to equal the distance from each u to its kth nearest neighbour [1] . In the former case the scale of localisation is fixed for all u in physical space, and in the latter it is fixed for all u in areas of a given density. Mapping the results for each location for some given h or k is an effective way of showing local changes in the distribution of some measured attribute, or changes in the relationships between several of these. However, a number of spatial processes operate at several scales simultaneously. Consider for example house prices which may exhibit patterns within streets, between parts of a town and between national regions, or topographic features whereby a local peak may be part of a larger valley when measured at a wider scale [20] . It can be helpful to consider the effect of varying either k or h in order to identify all scales at which patterns operate, particularly when spatial data are analysed in an exploratory situation. Fotheringham et al. [8] describe the process of so doing as involving a 'spatial microscope' whose focal length may be varied to allow the identification of patterns at different scales. For example, Foody [7] uses GWR to explore the relationship between species richness and three explanatory environmental variables in sub-Saharan Africa, and considers how spatial patterns in the geographically varying regression parameters change in association with h in order to investigate the underlying geographical scale of the relationships between these variables. Scale-space analysis [13] provides a multiscale framework for analysing data recorded in a regular rectangular array in this manner and is used for feature recognition. It may, along with other pixel-based approaches, be applied to data recorded in the kinds of irregular zones that are typical of many geographic data sets [17] .. While static mapping may be useful for investigating spatial variation for a fixed k or h [2] , visualizing variability of the spatial patterns with h, is arguably too complex a task for conventional cartography, particularly where multiple variables are considered concurrently. Interactive graphics provide opportunities for exploring complex structured data sets and generating knowledge from them [16] . For example, interactive graphical techniques have been developed to show the effects of scale on local surface derivatives [21] . Here we extend these ideas by developing complimentary graphical techniques, with coordinated behaviours and interactions through which these can be accessed. These new methods allow us to explore variations in h and are applicable to multivariate data sets measured using irregular zones. They are suitable for investigating the properties of spatial data at a range of scales. They include standard choropleth maps, maps of geographic weightings for any h (weighting maps) maps of geographically weighted means (gw-mean maps) and local variations from the mean (gw-residual maps), a localised (GW) version of the box-and-whisker plot that we term a gw-boxplot and a scalogram -a plot showing the variation of localised summary statistics as the value of h changes. Our prototype software contains interactions and visual encodings that are both geographic and geographically weighted. In combination these views and coordinated interactions are designed to help analysts gain insight into spatial patterns through which geographic processes may be characterised and understood.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Quasi-Interpolating Spline Models for Hexagonally-Sampled Data Abstract-The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. In this paper, we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient. To that aim, we deploy box-spline and hex-spline models, which are notably well adapted to hexagonal lattices. We also rely on the quasi-interpolation paradigm to design compelling prefilters; that is, the optimal filter for a prescribed design is found using recent results from approximation theory. The feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to Cartesian grid conversion problem. This work demonstrated the relevance of combining multidimensional splines with quasi-interpolation for reconstruction and resampling from data defined on 2-D lattices. We focused our study towards the hexagonal lattice, and proposed practical solutions with theoretically optimal FIR and IIR prefilters to be associated with box-splines and hex-splines. As confirmed by practical experiments, FIR and separable IIR quasi-interpolating prefilters achieve a particularly relevant tradeoff between the approximation quality and the required computation time.. Hence, quasi-interpolation should be considered as a viable alternative for all signal and image processing tasks in which there is an underlying reconstruction problem. Since box-splines and hex-splines are based on generic multidimensional concepts (vectors along the directions of the lattice for the box-splines, Voronoi cell for the hex-splines), it is straightforward to extend our approach to higher dimensional problems. For example, high-quality visualization of 3-D data, that is an active field of research [41] , could greatly benefit from our fast quasi-interpolating methods, because nontrivial interpolation is not tractable in 3-D. APPENDIX DERIVATION OF (25) Since , we just have to demonstrate (25) for . As shown in Fig. 10 , can be decomposed into three indicator functions that yield the three terms in the sum of (25) . Let us detail how we get the Fourier transform of the first one. This indicator function on the two rhomboids (each with surface area 1/3) is the sum of two box-splines (35) (36) (37) where we used . Stated as in Section III, the resampling problem amounts to estimating samples of the unknown function (the real-world luminance scene in the case of natural images) at new locations. In fact, if the target lattice is coarser than the initial lattice, annoying moiré patterns due to aliasing may appear. This problem can be avoided by lowpass filtering before sampling, with a filter whose cutoff frequency is adapted to the target lattice. Another suitable approach for such a case is a least-squares approach; i.e., a spline model that is the closest of in the sense, is fitted on the target lattice [25] . In this article, we considered the case of resampling onto the orthogonal lattice having the same density as , which allows us to neglect aliasing issues on the target lattice. This approach is also well suited when applying geometrical transformations, such as rotations or shears, gradient estimations, warping, and so on.. The presented approach is also appropriate for resampling onto a lattice with higher density, e.g., for zooming purpose. In Fig. 9 , we show the results obtained when resampling an image defined on the hexagonal lattice with density 1 onto a Cartesian grid with density 100, so as to magnify the properties of the surface in function of the chosen spline reconstruction space.. gives a piecewise constant model, while yields a surface composed of linear patches over triangles. For to be continuously differentiable, we have to rely on or . The result with is not reproduced, since it cannot be visually distinguished from the one with in Fig. 9(d) . Note how well the oblique contours are rendered with . For applications where derivatives have to be computed (edge detection ), or seem particularly adequate. The same zooming setup can also be applied to compare the intrinsic quality of sampling on a hexagonal versus Cartesian lattice. For that purpose, we make use of the zoneplate test image, whose analytical formula is given by (34) Samples on any source lattice (i.e., hexagonal and Cartesian of the same density) can be computed to obtain the initial measurements. The quantitative evaluation is then performed after upsampling this image (of size pixels) onto a fine Cartesian lattice with a density 100 times higher, and comparing these results against the sampled analytical formula on the fine grid. For upsampling the data from the hexagonal source lattice, we apply our box-spline methods (with interpolation and IIR1 prefilters), while for the Cartesian source lattice, we make use of separable B-splines (with interpolation and quasi-interpolation IIR prefilter as in [12] ). The box-splines and B-splines were chosen with the same order of approximation.. From the PSNR results in Table III , we observe that the hexagonal lattice is outperforming the Cartesian one, as also predicted by the theoretical analysis in [26] . Quasi-interpolation provides a substantial gain over interpolation, which shows that the theoretical asymptotical optimality of the IIR filters contributes to better resampling quality in practice. These results also demonstrate the superior quality that can be obtained by sampling on a hexagonal lattice.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A centrality-based topology control protocol for wireless mesh networks Nodes in wireless multi-hop networks establish links with their neighbors, which are used for data transmission. In general, in this kind of networks every node has the possibility of acting as a router, forwarding the received packets when they are not the final destination of the carried data. Due to the routing protocol procedures, when the network is quite dense the overload added by the routing management packets can be very high. To reduce the effects of this overload a topology control mechanism can be used, which can be implemented using different techniques. One of these techniques consists of enabling or disabling the routing functionality in every node. Many advantages result from selecting just a subset of nodes for routing tasks: reduction of collisions, protocol overhead, interference and energy consumption, better network organization and scalability. In this paper, a new protocol for topology control in wireless mesh networks is proposed. The protocol is based on the centrality metrics developed by social network analysts. Our target network is a wireless mesh network created by user hand-held devices. For this kind of networks, we aim to construct a connected dominating set that includes the most central nodes. The resulting performance using the three most common centrality measures (degree, closeness and betweenness) is evaluated. As we are working with dynamic and decentralized networks, a distributed implementation is also proposed and evaluated. Some simulations have been carried out to analyze the benefits of the proposed mechanism when reactive or proactive routing protocols are used. The results confirm that the use of the topology control contributes to a better network performance. Smart environments, smart devices, smart interaction, computing anytime and anywhere, ..., the accelerated development of information technologies and mobile devices results in people and/or "things" increasingly dependent on the online services offered through the Internet. In such scenario, Wireless Mesh Networks (WMNs) have evolved as a cost effective possible solution for user uninterrupted access to networking facilities. Valued features like robustness, reliability, easy deployment and maintenance, self-forming and self-configuration, make WMNs an important alternative to achieve an always-on connectivity. Among the three typical architectures of WMNs [1] , the present work focus on the client meshing one. In this case, the end-user devices are able to simultaneously provide application interface, routing and network configuration capabilities. Nowadays, the most common hand-held device used by an increasing number of people is the smart phone. The evolution of such mobile devices with their variety of embedded sensors results now in a not only communication equipment, but a complete sensing system [2] . Numerous applications are emerging in many fields like health, traffic, human behavior, environment monitoring, social networking and commerce [2] . With this perspective it is entirely feasible to consider a WMN composed by mobile phone users moving around a city as a cost-effective complement to commercial cellular networks. One of the major concerns in this kind of devices is related to their energy consumption. Therefore, optimization techniques that aim to reduce it are always required [3] .. Topology control techniques have been developed to improve the energy efficiency and the battery lifetime of a variety of networks. It also aims to reduce collisions, protocol overhead, and interference by means of a better control over the network connections and redundancy [4] . In general, there are three main types of topology control approaches [4] . First, power control techniques [5, 6] , adjust the communication range of the wireless nodes by means of the transmission power of their transceivers. This way, nodes are able to better manage their neighborhood size, interference level, power consumption and connectivity. Secondly, power mode mechanisms [7, 8] control the active or sleep operation modes of the nodes to dispense with redundant stations and still achieve the desired connectivity. Finally, hierarchical clustering approaches [9, 10, 11] aim to construct an efficient virtual backbone for data forwarding by the selection of a connected dominating set (CDS). From graph theory, a CDS of a graph is a connected subset in which all the nodes that does not pertain at that subset have at least one adjacent neighbor inside the subset. Due to the reduced number of nodes developing routing task, the main advantages of this CDS-based topology control are: collisions, protocol overhead and energy consumption reduction, efficient network organization and scalability improvement. In this work we evaluate an alternative method for this last category of topology control based on social network analysis metrics.. In this context, thanks to the increasing availability of network maps which depicts the behavior of complex systems and the universality of their characteristics [12] , network science appears as the renewed study of the structure and the dynamic behavior of a variety of networked systems [13] . Accordingly, social network analysts have developed an important set of measures and metrics which allow understanding the behavior and quantify the topology features of a diversity of networks [14] . Specifically, in this work we focus on centrality metrics developed to identify the most important actors (nodes) in a network by means of graph theory definitions and concepts.. In summary, the purpose of this work is to present and evaluate an alternative topology control mechanism based on centrality measures borrowed from social network analysis. This topology optimization has been applied to a client wireless mesh network formed with user hand-held devices.. The rest of the paper is organized as follows. In Section 2 we report and analyze the related work. Section 3 provides a background on centrality metrics. Section 4 presents and evaluates the proposed topology control mechanism. A performance evaluation has been carried out by means of simulations, taking into account both reactive and proactive routing protocols. The results are presented in Section 5. Finally, the conclusions and future works are summarized in Section 6. In this paper we have evaluated the feasibility of using the centrality metrics from social network analysis to create a topology control mechanism based on a connected dominating set. Specifically, for a dynamic wireless mesh network formed by user hand-held devices, we have proposed and evaluated some mechanisms to select which of those devices must act as routers, forwarding the packets received from other handheld to their destination. The mechanism implementation has been proposed in two ways, centralized and distributed. For the centralized approach, we have evaluated the three most common centrality measures: degree, closeness and betweenness centrality. In all those cases, the more central nodes have been selected to form the backbone. The experimental analysis has shown that the network fragmentation using the betweenness centrality is considerably lesser than the resultant with degree or closeness centralities. Thus, it is possible to conclude that by far the betweenness centrality is the metric that better identifies the stations that should be considered for routing tasks. In the second place, taking into consideration that a centralized implementation could be unfeasible in most scenarios, a distributed implementation has been proposed. In this case only the betweenness centrality has been considered. To distribute the responsibility, the concept of the egocentric network perspective of each station is needed. That is, every station computes its own centrality knowing only its own established links (neighbors). Besides, due to the dynamic and time evolving nature of the network with which we are dealing, we also discuss and evaluate different distributed mechanisms to select the central stations that will act as routers. First of all, every station selects the node in its neighborhood with the highest centrality. This mechanism works well in most cases if a minimum density of nodes exists. Then again, the complete connectivity is not assured. To guarantee that connectivity, some approaches have been proposed and compared in terms of overload and effectiveness. As a future line of work, the minimum number of routers per neighborhood needed to guaranty a desired connectivity in the distributed implementation will be studied.. The effectiveness of this centrality-aware topology control protocol has been verified through extensive simulations. The evaluation has been carried out for both reactive and proactive path selection modes. For all the studied cases the efficiency of the network was improved or at least remain equal but always with a considerably lower amount of transmission/reception energy consumption. Another common factor in all the simulation results is the reduction of the packet end-to-end delays. This is a direct consequence of the global bit-rate savings which implies lower channel contention. The reduction of the number of mesh stations involved in the path selection procedure also improves the scalability when the variability of the network demands faster path updates. Finally, we confirm that greater energy savings are obtained in the proactive path selection case because of the greater overhead present with this operation mode.. As current and future lines of work we are carrying out performance evaluations considering human mobility models. Besides, we are designing and evaluating a multi-metric protocol which assigns different weights to the egocentric betweenness centrality and the node remaining energy values. Nowadays, the application of complex networks techniques and social network analysis concepts to improve the performance of wireless ad hoc networks is growing as a fertile research area [15] . Some recent works are summarized in the following. [16, 17, 18] apply the small world phenomena, re-popularized by [19] , to reduce the average path length of the network. The basic idea of these proposals is to modify the physical topology of the network based on the social features of the underlying graph. The small world property (or low average path length) could be achieved either by the aggregation of long-ranged links [17] or by a combination of rewiring, deletion and/or addition of links/nodes [16] . Authors in [18] combine centrality measures with directional beamforming to create long-range links between more central nodes. The same authors extend their study to sparse highly partitioned networks in [20] .. SimBet [21] is a routing protocol designed for delay-tolerant MANETs. It uses two social network analysis metrics (centrality and similarity) for message forwarding decisions. Betweenness centrality is selected to identify more suitable bridge nodes, and the similarity measure is used to find nodes that are closer to the destination neighborhood. A utility function combines the similarity and the betweenness utilities and allows adjusting the relative importance of them. For performance evaluation both utilities has been assigned the same importance. For their part, authors in [22] apply social network analysis metrics to detect critical

O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O


An initial exploration of the link relationship between UK university Web sites Aggregates of links are of interest to information scientists in the same way as citation counts are: as potential sources of data from which new knowledge can be mined. The recent discovery of a correlation between a web link count measure and the research quality of British universities is built upon by applying a range of multivariate statistical techniques to counts of links between pairs of universities. This represents an initial attempt at developing an understanding of this phenomenon. Plausible results are extracted, including the high degree of similarity between the Scottish universities and limited evidence of a dichotomy between new and traditional universities. Outliers in the data were also identified by the techniques, some of which were verified by being tracked down to identifiable web phenomena. This is an important outcome because successful anomaly identification is a precondition to more effective analysis of this kind of data. The identification of groupings is encouraging evidence that web links between universities can be mined for significant results, although it is clear that more methodological development is needed if any but the simplest patterns are to be extracted. Finally, based upon the types of patterns extracted it is argued that none of the methods used are capable of fully analysing link structures on their own. Web links are potential indicators and generators of trust (Davenport and Cronin, 2000) , with a page that is the target of many being more likely to contain useful information than one that is not. The analogy with citations is clear and has been remarked upon many times, as has the fact that web links are less reliable than citations due to the lack of quality control over the vast majority of the Web (Egghe, 2000; Bar-Ilan, 2001; Björneborn and Ingwersen, 2001; Thelwall, 2001a) . A correlation has been recently discovered, however, between a link count measure and research ratings (Thelwall, 2001a) for British universities. This result shows that meaningful information can be extracted from large-scale comparisons of web links between academic websites, although the results are far from reliable on the level of individual universities. In fact these results were obtained despite the finding that relatively few links were targeted at online academic papers, making the interpretation of link counts highly problematic and necessitating further exploratory research. Given the positive results, there is an exciting opportunity to develop new tools to analyse the same kind of data in order to extract more information and to gain a deeper insight into the underlying processes involved. This paper represents a first attempt to develop an understanding of the individual academic website interlinking phenomenon.. There have been several studies of web links in electronic journals and other areas of the Web, many through direct analogy with citations. Studies of e-journals have, so far, not found it possible to get meaningful results from attempts to extend the journal impact factor metric to a backlink-based equivalent (Smith, 1999; Harter and Ford, 2000) . It was, however, a generalisation of this, Ingwersen's Web Impact Factor (WIF) that has been shown to correlate with university research ratings when applied to their websites (Thelwall, 2001a; Thelwall, 2002) . This example shows that web link aggregation is a technique that has the potential to reveal meaningful underlying trends, in spite of the following serious concerns over many aspects of the validity of such data.. • The search engines often used to collect the data have been found to be unreliable (Bar-Ilan, 1999; Rousseau, 1999; Snyder and Rosenbaum, 1999; Thelwall, 2000) , although recent improvements have been identified in AltaVista (Thelwall, 2001b; Thelwall, 2001a ).. • Web pages are not subject to quality control in the way that journal articles are.. • Web pages can have multiple URLs. Entire collections of web pages can also be multiply sited in a common process known as mirroring.. • The authors of pages can be difficult to identify, and authorship may, as in the case of many traditional journal articles (Cronin, 2001) , be a complex concept.. • Web pages can appear and disappear instantly, even in their thousands, as a result of a single decision (Thelwall, 2001c ).. • Counts of web pages are affected by stylistic considerations: an author may publish an online book, for example, as a single huge web page or thousands of small pages.. One previous study has applied multivariate statistical analyses to websites, that of Larson (1996) . This study chose sites from a common area, Earth Sciences, and used a cocitation analysis based upon counting pages that link to pairs of chosen sites.. Larson produced a plausible subject-based map using multi-dimensional scaling, but his approach does not seem to have spawned any imitators. Björneborn and Ingwersen (2001) have also proposed new web methods that are based, in part, upon bibliometric methodologies, and use ideas from graph theory. Chen et al. (1998) have already studied the web link interconnection between a small subgroup of British universities, using pathfinder network diagrams rather than a group of statistical analysis tools. Thelwall (2001d) has applied non-statistical graphical network techniques to general web domains.. This exploratory study will apply four common multivariate statistical analysis techniques to counts of links between a set of academic websites in order to seek to describe in a useful way the web relationships between them. The sites chosen are from 96 British public university institutions. Britain is an acceptable source because its number of universities gives a data set large enough for meaningful statistical analysis, but just small enough for the 96 x 96 -96 = 9120 link counts to be obtained. The analysis would not be appropriate for countries with small numbers of universities, but those with larger numbers could work with an appropriately sized coherent subset. The primary research problem is to ascertain whether the statistical techniques are capable of extracting meaningful information from the data sets, in terms of being able to be mapped to plausible real world phenomena. The secondary problem is to discover whether they can be used to reveal the existence of outliers in the data that can be verified through the identification of a cause. Essentially, both the appropriateness of the techniques and the quality of the data are being tested here. This is expected to be the first step in the much longer project of understanding and successfully exploiting this kind of web link data. The statistical techniques used have pointed to the underlying data structure being determined by both geography and research. The actual link counts also revealed large anomalies with identifiable causes. The conclusion was reached that although patterns were present in the data, none of the techniques covered were fully adequate to extract them, although all could be expected to provide partial results in certain situations. Further methodological developments are therefore needed. Due to the combination of the anomalies in the data with the graduated research and geographic components, it is likely that a combination of approaches will be necessary to mine more trends from the data. One possible approach is to have an initial data cleansing phase, where anomalies are identified and dealt with, followed by pattern extraction, perhaps using different techniques. The pattern extraction could also be undertaken in two phases, one for research and one for geography. Ultimately, if both of these were successful, the residual trends would point to patterns that would perhaps be the most interesting of all, reflecting less-readily identifiable phenomena.. The results in this paper have served to highlight the issues that must be resolved in order to mine university-university web link count data and it is hoped that the results will form a stepping-stone for the creation of a set of more effective techniques.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A novel hybrid artificial bee colony algorithm with crossover operator for numerical optimization Abstract Artificial Bee Colony (ABC) algorithm is one of the most recently introduced swarm intelligence algorithms which inspired by the foraging behavior of honey bee swarms. It has been widely used in numerical and engineering optimization problems. This paper presents a hybrid artificial bee colony (HABC) model to improve the canonical ABC algorithm. The main idea of HABC is to enhance the information exchange between bees by introducing the crossover operator of genetic algorithm to ABC. With suitable crossover operation, valuable information is fully utilized and it is expected that the algorithm can converge faster and more accurate. Eight versions of HABC algorithm combined by different selection and crossover methods under the model were proposed and tested on several benchmark functions. Then, the settings of the new parameter crossover rate for two well performed HABC versions are tested to verify their best values. Finally, four rotated functions and four shifted functions are used to test the performance of the two algorithms on complex functions and asymmetric functions. Experiment results showed that these two versions of HABC algorithm offer significant improvement over the original ABC and are superior to other two state of the art algorithms on some functions.Keywords Artificial Bee Colony Á Hybrid artificial bee colony Á Crossover operator Á Crossover rate 1 Introduction Population-based optimization algorithms are a kind of optimization technique which is used to find near-optimal solutions to the complex numerical and engineering optimization problems. In population-based optimization algorithms, the population is consisting of a certain number of individuals and each individual presents a solution of the problem to be solved. In each iteration, the population is modified by applying some operators on these solutions depending on their fitness information. Hence, the population moves towards better solution areas of the search space.. Two important branches of population-based optimization algorithms are swarm intelligence (SI) algorithms and evolutionary algorithms (EA). SI is an innovative computational intelligence technique inspired by intelligent behaviors of insect or animal groups in nature, such as colonies of ants, flocks of birds, swarms of bees, and so on. In recent years, many SI algorithms have been proposed, such as ant colony optimization (ACO) (Dorigo and Gambardella 1997) , particle swarm optimization (Kennedy and Eberhart 1995) , bacterial foraging optimization (BFO) (Passino 2002) and immune algorithm (IA) (Gong et al. 2010) . Artificial Bee Colony (ABC) algorithm is a novel swarm intelligent algorithm inspired by the foraging behaviors of honeybees. It was first introduced by Karaboga (2005) . Due to the advantages of simple in concept, easy to implement and remarkable optimization ability, ABC and its variants have attracted the attention of researchers and been widely used for solving many numerical optimization (Karaboga and Basturk 2007a) and engineering application problems, such as neural networktraining (Karaboga et al. 2007; Ozkan et al. 2011) , electrical engineering optimization (Rao 2010; Ravi and Duraiswamy 2011) , scheduling optimization Ziarati et al. 2011) , civil engineering (Sonmez 2011; Mandal et al. 2012) , data diming (Karaboga and Ozturk 2011; Yan et al. 2012 ) and image processing (Ma et al. 2011; Chidambaram and Lopes 2009) .. However, the speed of convergence of ABC decrease as the dimension of the problem increases (Karaboga and Basturk 2007a) . This is mainly because in the ABC algorithm, bees exchange information on one dimension with a random neighbor in each food source searching process. In this work, a hybrid artificial bee colony (HABC) algorithm mode is founded. In the model, the crossover operator of genetic algorithm (GA) is introduced to improve the canonical ABC in solving optimization problems. Eight versions of HABC algorithm combined by different selection and crossover methods under the model are proposed and tested.. The rest of the paper is organized as follows. In Sect. 2, we will introduce the canonical ABC algorithm. Section 3 will discuss how crossover operator is used in ABC. Our HABC model and algorithms will be given in this section. In Sect. 4, three experiments will be done. The first experiment tests the ABC, HABC and a comparison algorithm on several basic benchmark functions. The second experiment tests the setting of new parameter for two typical versions of HABC algorithm which performed well in experiment 1. A further test with statistical analysis is done in experiment 3. More benchmark functions were used including four rotated ones. The results are presented and discussed. Finally, conclusions are drawn in Sect. 5. This paper presents a HABC model, in which the crossover operator of GA is introduced to improve the original ABC algorithm. Eight versions of HABC algorithm with combination of different selection methods and crossover methods under the model are proposed. Three experiments were done to verify the optimizing ability of proposed HABC variants. The eight versions of HABC algorithm were tested on several basic benchmark functions compared with standard ABC and DMS-PSO-HS firstly. The results showed that HABC6, HABC7, HABC8, HABC5 (all use the arithmetic crossover method) and HABC3 (select the medial food sources and use one point crossover method) performed better than the canonical ABC on most functions. Especially the HABC6, it obtained definitely good results on most functions compared with the other algorithms. Meanwhile, the results showed that algorithms with arithmetic crossover method are not that sensitive to the selection method. Therefore HABC7, HABC8 and HABC5 can be represented by HABC6. The two functions that HABC3 didn't perform well on are all unimodal nonseparable functions and there was no such regularity for HABC6. The best crossover rate settings for two representative algorithms-HABC6 and HABC3 were tested. It is shown from the results that best CR value for HABC6 is 1.0 and best CR value for HABC3 is 0.05. With CR value of 1.0, selecting method is meaningless for the four HABC algorithms which using the arithmetic crossover method. So the four algorithms can be unified as HABC6, which coincide with the phenomenon mentioned above. In additional, under this CR value, HABC6 improved its results further more than that in experiment 1. A further test is done for HABC6 and HABC3 on four rotated functions and four shifted functions. HABC6 performed very well on rotated functions but worse on shifted functions. HABC3 performed not that well on common and rotated functions compared HABC6. However, it performed better than original ABC on most functions. Especially on shifted functions, it performed best on a few functions.. In overall, the HABC algorithm employs one more control parameter CR to add a crossover operator in the canonical ABC algorithm. With the new operator, bees exchange more information in the early stage of the algorithm, which enhances the searching ability of the algorithm. At the end of the algorithm, as the differences between individuals' decrease, the perturbation of crossover operator decreases, too. The results in three experiments show that two typical HABC variants HABC6 and HABC3 outperform the canonical ABC on a large amount of benchmark functions in terms of accuracy, robustness, and convergence speed. For those functions global best are not in their center, HABC3 is recommended as it has better robustness. The mean and standard deviations of function values obtained by HABC6 and HABC3 on benchmark functions with different CR values are given in Tables 5 and 6. All tests were run for 30 times and ended after 100,000 FEs. Best values obtained by the algorithms for each function were marked as bold. It has mentioned above, HABC6 can find the global minimum 0 on Rastrigin and Griewank. The mean FEs they reached the global minimum is recorded and attached after their mean values on these two functions.. The mean best function value profiles of HABC6 with different CR values on seven benchmark functions are shown in Fig. 3 . With CR of 1.0, HABC6 obtained the best mean results on five functions. On the other two functions Rosenbrock and Schwefel, best results are obtained with CR of 0.05.. On Sphere and Quadric functions, HABC6 have better results as well as better convergence performance with a higher CR, as seen in Fig. 3a, c .. On Rastrigin and Griewank, HABC6 with different CR values all found the global minimum 0. However, it can be seen from Fig. 3d , g, with larger CR values, the algorithms converged faster. Similar phenomenon occurred on Ackley function. Algorithms with different CR values all trapped in local minimum but better convergence performances were shown with larger CR values.. Rosenbrock and Schwefel are the two functions that HABC6 didn't perform well in experiment 1. Same phenomenon occurred in experiment 2. On Rosenbrock, all tests trapped in local minimum, as seen in Fig. 3b . The results got worse as the CR increased. However, they have little difference with each other. At the meanwhile, the algorithm converged faster with larger CR values in the early stage. On Schwefel, worse results and convergence performances were obtained with larger CR, as shown in Fig. 3e .. It can be concluded that 1.0 is the most suitable CR value for HABC6 because the algorithm performed excellently under this value on those functions it could solve successfully. Under CR of 1.0, the results were improved greatly compared with that in experiment 1 on the five functions.. Moreover, it is worth noting that, with CR value of 1.0, HABC5, HABC7 and HABC8 can be regarded the same as HABC6. The four algorithms using the arithmetic crossover methods get unified. This may explain the supposition made in experiment 1: algorithms with arithmetic crossover method are not that sensitive to the selection method.. Compared with HABC6, the differences of results for HABC3 with different CR values are not that significant, especially with CR values of 0.02, 0.05 and 0.15. Their profiles are nearly the same on convergence plots. As a result, we use the box plots instead of the convergence Fig. 4 . It can be seen from the Table 6 , with CR of 0.05, HABC3 obtained the best mean results on five functions. On the other two functions, best results are obtained with CR of 0.02.. It is obvious that HABC3 with CR of 0.05 had a better convergence performance compared with the other values on Quadric, Schwefel, Ackley and Griewank functions, seen in Fig. 4c , e, f, g. On Sphere and Rastrigin functions, HABC3 with CR of 0.05 is only a little worse than with CR of 0.02. As a result, we can conclude that best CR value for HABC3 is 0.05. It has mentioned above that eight versions of HABC algorithm have been proposed in this paper. They will be tested on several benchmark functions firstly. Canonical ABC and a PSO variant-dynamic multi-swarm particle swarm optimizer with harmony search (DMS-PSO-HS) (Zhao et al. 2011 ) are used for comparison. Then, as the new parameter CR is introduced in HABC algorithms, the setting of CR on two typical HABC will be tested. Finally, a further statistical test will be done on ten more benchmark functions including four rotated functions to verify the optimization ability of the two typical HABC algorithms. Besides ABC and DMS-PSO-HS, differential evolution algorithm with ensemble of parameters and mutation strategies (EPSDE) (Mallipeddi et al. 2011) , which is a variant of differential evolution (DE) (Storn and Price 1997) , is also employed as comparison. The codes of DMS-PSO-HS and EPSDE algorithms were provided by Professor P. N. Suganthan of Nanyang Technological University. All algorithms were run in Matlab 2010b using computer with Intel Core 2 Duo CPU E4500, 2.20 GHz, 1 GB RAM. The operating system of the computer is Windows XP.

O O O B I I O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O B I I O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The Intra-Americas Sea Low-level Jet A relevant climate feature of the Intra-Americas Sea (IAS) is the low-level jet (IALLJ) dominating the IAS circulation, both in summer and winter; and yet it is practically unknown with regard to its nature, structure, interactions with mid-latitude and tropical phenomena, and its role in regional weather and climate. This paper updates IALLJ current knowledge and its contribution to IAS circulation-precipitation patterns and presents recent findings about the IALLJ based on first in situ observations during • C. The atmospheric mixed layer height reached 1 km near the surface wind maximum below the IALLJC. Observations indicate that primary water vapor advection takes place in a shallow layer between the IALLJC and the ocean surface. Latent heat flux peaked below the IALLJC. Neither the reanalysis nor MM5 captured the observed thermodynamic and kinematic IALLJ structure. So far, IALLJ knowledge is based on either dynamically initialized data or simulations of global (regional) models, which implies that a more systematic and scientific approach is needed to improve it. The Intra-Americas Study of Climate Processes is a great regional opportunity to address trough field work, modeling, and process studies, many of the IALLJ unknown features. Relatively fast-moving currents of geophysical fluids are not unusual in nature. The West Wind Drift (WWD), an ocean current that moves from west to east encircling Antarctica; the Kuroshio Current, the world's second largest current (after the WWD), an oceanic stream found in the western Pacific Ocean off the east coast of Taiwan and flowing northeastward past Japan; and the Gulf Stream in the Atlantic Ocean are just three samples of somewhat rapid-moving salty water currents. The WWD impedes warm waters from reaching the polar caps, while the other two are important in transporting warm tropical waters northward.. Fast-moving air or jet streams have been known to exist in the atmosphere for decades. The major atmospheric wind currents, the polar and subtropical jet streams, are westerly winds at approximately 10 and 13 km high, respectively, in both the Northern Hemisphere and the Southern Hemisphere. These jets can attain mean wind speeds in the range of 15-20 to 30-35 m s −1 , depending on the season and hemisphere. Many jet streams in the Earth's atmosphere are thousands of kilometers long, hundreds of kilometers wide, and several kilometers in depth, and their variability, both in space and time, is significant. In the atmosphere, jets have been observed at different levels, in distinct seasons, and in many regions around the globe. Stensrud 1 discusses in detail the wide range of atmospheric phenomena at lower layers that have been described in the scientific literature as low-level jets (LLJs). In the summer, LLJs usually weaker in strength than the upper jet streams, can form in tropical regions near the top of the boundary layer (BL) or in the lower troposphere. Examples of atmospheric LLJs are the Somali Jet (SJ) in east Africa, a cross-equatorial flow from south to north for which Bunker 2 and Findlater 3 were the first to draw scientific attention to and in the Americas, the Great Planes LLJ (GPLLJ), documented by Hoecker Jr. 4 and later by Bonner, 5 and the LLJ just off the west coast of subtropical South America over the Pacific. [6] [7] [8] In general, the atmospheric jet streams, through a series of convergence-divergence patterns, can strongly influence synoptic-scale weather systems in mid and higher latitudes and in the tropics. The LLJs, as their counterpart in upper levels, are also very relevant to climate. 1 These strong currents also play an important role in the global heat, angular momentum, and kinetic energy budgets. 9, 10 In lower levels, the SJ accounts for nearly half the interhemispheric mass transport in the lower troposphere around the world. 2 The dynamic conditions capable of forming and maintaining (especially at lower levels from breaking up against mixing and dissipative forces) such strong air currents are, in general, quite variable depending on fluid characteristics and on external forcing. Several mechanisms, such as thermal gradients over sloping terrains, planetary boundary layer (PBL) oscillations, 11 and land-surface features, have been proposed to explain LLJs immersed in a dormant environment. Large-scale forcing, such as the coupling of upper jet streams with LLJs, their interaction with convective activity, 12 and the synoptic and subsynoptic-scale environment, have been analyzed to explain observed events of the GPLLJ. 13 In the Americas, some of these jet streams, such as the Gulf of California (GC) LLJ, [14] [15] [16] [17] the Chocó jet (CJ) in the eastern tropical Pacific (ETP), 18 and the GPLLJ, have been intensively studied through observations 3, 4, 16, 17, [19] [20] [21] and numerical studies. [22] [23] [24] Regional or global scale experiments have provided significant ocean, land, and atmospheric data to study the structure and dynamics of some LLJs. Meteorology has benefited from such experiments as the Global Atmospheric Research Program (GARP) in the 1960s and the GARP Atlantic Tropical Experiment (GATE) in the 1970s 25, 26 ; the latter has particularly benefited meteorology with regards to the interaction between the West Africa (WA) LLJ and easterly waves 27, 28 and from advances in the understanding of hurricane processes (formation, structure, and role in the circulation) in the tropical Atlantic. 29 More recently, the North American Monsoon Experiment (NAME), conducted in the summer of 2004, 30, 31 provided valuable data to analyze the North American Monsoon System (NAMS), the associated LLJs (GCLLJ and GPLLJ), and the summer precipitation distribution. [32] [33] [34] [35] Although there have been a considerable number of meteorological research programs/ field campaigns covering the tropical and subtropical Americas in the last decades, such as GARP (1960s-), GATE (1974) , the Global Weather Experiment (1978) (1979) , the World Ocean Circulation Experiment (1990) (1991) (1992) (1993) (1994) (1995) (1996) (1997) (1998) , and some regional or local experiments, such as the Atlantic Trade Wind Experiment (1969 36 ), the Barbados Oceanographic and Meteorological Experiment (1969 37 ), the Venezuelan International Meteorological and Hydrological Experiment (1969, 1972 38 ), NAME, 30, 31 and the Eastern Pacific Investigation of Climate Processes in the Coupled Ocean-Atmosphere System (2000- 39 ) , the Caribbean region remains to be one of the less-studied areas in the world, despite its societal importance from impacts of many meteorological and climate systems. The Caribbean is home to more than one hundred million people, many of them living in relatively small island states, some of which are among the poorest in the Americas and the world.. Traveling easterly waves, 40 tropical storms and hurricane activity, 41 convective systems, 42 cold fronts reaching tropical regions, 43 ,44 the mid-summer drought (MSD; canícula or veranillo), 45 the warm pools, 46 ,47 the trades, and an intense LLJ, 48 are just some of the meteorological and or climate features that make this region worth studying in the context of an integrated (observations, modeling, processes studies) research program. In this respect, a group of scientists from countries of the region have been working on a Science and Implementation Plan for the Intra-Americas Study of Climate Processes (IASCLIP), to be executed in the near future within the Variability of the American Monsoon (VAMOS) Climate Variability (CLIVAR) Program.. The Caribbean has a unique environment for a remarkable range of meteorological phenomena, such as easterly waves, hurricanes, temporales (periods of weak to moderate rainfall lasting several days), MSD, cold fronts, trade surges, and northerlies, most of which are very little understood in the context of regional weather and climate. One of the most relevant features of this region, practically unknown with regard to its nature, structure, interaction with other regional phenomena of the tropics and extratropics, or in relation to its role in weather and climate, is a LLJ that dominates the Caribbean circulation, both in summer [48] [49] [50] and winter, 51, 52 which is called the Intra-Americas Sea (IAS) LLJ (IALLJ). Although some evidence of the existence of a wind maximum near the ocean surface can be inferred from previous work 53 or a jet had been suspected to occur in a nearby area where it is currently observed, 1 there seems to be no scientific reference or documentation of the IALLJ before the work of Amador.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Probabilistic multi-path vs. deterministic single-path protocols for dynamic ad-hoc network scenarios We investigate the performance of different protocol stacks under various application scenarios. Our method of choice is a full-fledged simulation in QualNet, testing the complete protocol stack over fairly large-scale networks. We find that the relative ranking of protocols strongly depends on the network scenario, the session load, the mobility level, and the choice of protocol parameters. We show that the Parametric Probabilistic Protocols, which we generalize from their original definition, can outperform standard routing protocols, such as AODV or Gossiping or Shortest-Path, in a variety of realistic scenarios. In the world of wireless communication, it would be wonderful to have a single, simple protocol that worked perfectly under any conditions, but protocols all behave differently in different circumstances. Every scenario has properties that can make one protocol inherently better than another. Examples of this include situations with static networks compared to cases with frequent or significant topology changes, or extreme cases of data flow, such as a network with a single uplink node compared to a network where all nodes are peers and communicate with each other. Dynamic topology is an especially important factor in wireless networks, and can be induced by node failures or temporary power loss, device mobility, or signal interference. Network load is another major discriminator: a protocol that produces the least load when there is very much network traffic may not do so when there is very little.. In this paper, we undertake a systematic empirical analysis of the most commonly referenced application scenarios for ad-hoc wireless network communication. We consider three different scenarios: (i) alarm and mapping tasks for sensor networks with a single destination node that needs to be reached, (ii) full any-to-any networking with all network nodes as possible sources and destinations, and (iii) a futuristic, but likely most realistic, multiple-basestation scenario with nodes connecting to one of several equivalent uplink destinations (i.e., base stations) in an ad hoc fashion.. We take a holistic view of the protocol stack (i.e., optimizing the whole stack rather than individual layers) from the data link to the network layer. As MAC protocols, we study CSMA and 802.11, and to a lesser extent, TDMA. On the routing layer we include some well-known protocols: AODV, Shortest-Path, Gossiping, and Flooding. We also consider a generalization of Parametric Probabilistic Routing (PPR), introduced in [3] as a family of multi-path routing protocols whose members are characterized by the function describing the probability of forwarding received messages. We design a generic form of the PPR retransmission probability that merges the two major protocol classes in [3] and Gossiping. We also provide a more intuitive explanation of the parameters in the retransmission function in one of the classes. Interaction between layers in a protocol stack have important performance implications. In [2] , statistical methods to formally characterize the interaction between the MAC and the routing layers have been used. The objective of our experimental analysis is to study the combination of MAC/routing protocols that works best for a given scenario, session load and mobility, and to test the efficacy of our modified form of PPR in real-world simulations.. We use simulations to carry out our empirical analysis. All protocols are fully implemented in the network simulator QualNet [18] , in which we simulate the entire protocol stack across a very large parameter space. A key finding is that the ranking of the routing protocols changes with increasing mobility for most scenarios, where a scenario is defined by a multitude of parameters. Intuitively, this prominent role of mobility is due to the fact that the protocols rely (to different extents) on the accuracy of global information (such as hop distance information) that is propagated through the net-work by various means; this accuracy is crucially impacted by mobility. Our experiments are also grouped into three main scenarios in which we present a detailed comparison of the diverse protocols. We find that Shortest-Path wins in terms of best performance for low mobility in the singledestination scenario; AODV wins in any-to-any networks with no or low mobility, Gossiping wins in any-to-any networks for high mobility values; Directed-Transmission wins at all mobility levels in multiple-destination scenarios and in the high-mobility single-destination scenario.. Related Work. The work most closely related to ours is [3] , where Parametric Probabilistic Sensor Network Routing was proposed and tested in a light-weight simulation environment, not taking into account issues of dissemination of global data or protocol layers other than routing. In addition to consideration of mobility and other classes of scenarios than simple sensor networks, the present simulation results are done using a full-fledged implementation including information distribution models and all network layers. Routing in wireless and ad hoc networks has been the subject of active research for quite some time; see [15] for the state of the art until 1995 and more recent survey papers [14, 5, 12] . Probabilistic routing and Gossiping have been applied in various setting, such as spreading distributed database updates [6] and multicast techniques (see [11] for a recent result and an overview). Non-constant probability Gossiping has been developed by Kempe et al. [9] , in which the authors use a Gossip-based approach to spread alarm messages, where the probability of forwarding to a particular neighbor depends on the geographic distance to that neighbor. Multiple path routing has been applied in [7] in order to make a network resilient against node failures.. Organization. The remainder of this paper is organized as follows. We propose a generalization to the idea of Parametric Probabilistic Routing in Section 2. Section 3 presents the remaining protocols that we study in more detail. The different scenarios that we study are introduced in detail in Section 4. The setup of our simulations is explained in Section 5 and the results are given in detail in Section 6. Concluding remarks are in Section 7. In addition to formalizing the Parametric Probabilistic Routing protocols introduced by [3] , through a comprehensive set of realistic simulations, we have demonstrated the importance of considering the dependence of performance on topology changes through mobility, and on the scenario being simulated (Figures 2 and 3) . We have also investigated the effect of the total session load (Figure 4 ) and number of packets in a session ( Figure 5 ). Due to space limits, we only present a sample of the most interesting results; additional plots are available from the authors. We evaluate the effect of mobility in a separate subsection before discussing the results for the three different application scenarios in detail. The effect of the number of packets per session is shown only in the context of the any-to-any scenario, and the effect of the number of sessions is shown only in the context of the single destination. Except for Figure 4 , all figures show experiments of 1000 packets with other parameters shown on the axes or as separate curves.

O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O B O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Meditation improves self-regulation over the life span The use of meditation to improve emotion and attention regulation has a long history in Asia and there are many practitioners in Western countries. Much of the evidence on the effectiveness of meditation is either anecdotal or a comparison of long-term meditators with controls matched in age and health. Recently, it has been possible to establish changes in self-regulation in undergraduate students after only 5 days of meditation practice, allowing randomized trials comparing effects of meditation with other self-control methods such as relaxation training. Early studies took place in Chinese universities; however, similar effects have been obtained with U.S. undergraduates, and with Chinese children aged 4.5 years and older Chinese participants aged 65 years. Studies using neuroimaging techniques have shown that meditation improves activation and connectivity in brain areas related to self-regulation, and these findings may provide an opportunity to examine remediation of mental disorders in a new light. Mindfulness-based interventions (MBIs) are composed of several key components, including relaxation, breathing practice, mental imagery, and body-mind awareness. [1] [2] [3] [4] [5] Although MBIs vary in their methods, quality, and dosage, some have been shown to improve attention, emotion regulation, and social relationships in children and adults. 1, [4] [5] [6] [7] However, several key theoretical and methodological challenges arise in the field. 8 As noted in a recent review, 9 most research in this area has lacked scientific rigor and has not used the random assignment and active control necessary to attribute causality to the mindfulness intervention. One reason that most studies do not use these designs is the expectation that very long-term training is needed to obtain strong behavioral results. In this paper, we examine one form of mindfulness training for which extensive randomized trials have been conducted using a rigorous control of relaxation training. These studies have provided a possible anatomical basis for the effects of training involving both central and autonomic nervous system changes. These anatomical changes suggest the possibility of an approach to the remediation or prevention of some clinical conditions, including substance abuse, psychopathy, borderline personality disorder, and schizophrenia. Mindfulness mediation has proven effective in improving brain functions related to executive attention in normal subjects across the life span. Our studies of IBMT suggest its utility in improving the activity and connectivity of the executive attention network involved in self-regulation. This network can also be improved by exercises that involve its repeated use. The evidence discussed here supports the use of attention training and meditation to improve the lives of children and as a possible treatment of a variety of conditions that may involve a deficit in self-regulation.

B O B O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B


NP-hardness of Euclidean sum-of-squares clustering Abstract A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al.


Some recent results on Ramsey-type numbers In this paper we survey the authors' recent results on quantitative extensions of Ramsey theory. In particular, we discuss our recent results on Folkman numbers, induced bipartite Ramsey graphs, and explicit constructions of Ramsey graphs. Ramsey theory can be loosely described as the study of structure which is preserved under finite decomposition. Its underlying philosophy is captured succinctly by the statement ''Complete disorder is impossible''. Since the publication of the seminal paper of Ramsey [31] in 1930, the subject has grown with increasing vitality. For more information about Ramsey theory, see e.g., [21, 22] .

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A field study of end user computing: findings and issues AbstractThis article reports on a series of interviews on end user computing carried out in twenty locations in The growth of end user computing is one of the significant phenomena of the 1 980s in the information management world. A recent study by the International Data Corporation predicted that four out of five administrative and professional workers will be using personal computing to support their work and personal activities by 1990 [3] . In a study published in 1981, Rockart and Flannery referred to estimates that while current end user computing consumed about ten percent of computer capacity in large corporations, such use would grow to consume seventy percent of an expanded capacity by the end of the decade [4] . Business Week, in November 1982, predicted that 26 million executives, professionals, and hobbyists would own microcomputers by 1985. In the same article, Business Week quotes an estimate from Dataquest, Inc. that the training industry will capture $3 billion of the $14 billion spent on personal computers by 1986 [1] .. But what is actually happening in the world of end user computing? Will its growth be as explosive as the predictions? Rockart and Flannery see lesso~s from the Gibson-Nolan stage theory [2] in the management of end user computing. They warn that while most companies are still (1981 ) the "initiation" or early "contagion" stages of the curve, the most adverse effects of the "control" stage may ensue unless significant attention is paid to managing end user computing [4] .. In the fall of 1982 the Center for the Study of Data Processing at Washington University in St. Louis, encouraged by its Corporate Affiliates, began a research project to examine the state and direction of end user computing in the St. Louis corporate environment. The goal of the project was to gather information and gain perspective for planning educational programs for end users, and developing strategies for the management of end user computing. With the growing demand ior ~omputing capabilities, input was needed directly from the managers who were either already involved in interactive computing or planning for such capability.. This article reports on a series of interviews carried out between December 1982 and March 1983 with managers and professionals in twenty locations. It attempts to describe the varieties of

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Dominating Induced Matchings for P 7-Free Graphs in Linear Time Let G be a finite undirected graph with edge set E. An edge set E ⊆ E is an induced matching in G if the pairwise distance of the edges of E in G is at least two; E is dominating in G if every edge e ∈ E \ E intersects some edge in E . The Dominating Induced Matching Problem (DIM, for short) asks for the existence of an induced matching E which is also dominating in G; this problem is also known as the Efficient Edge Domination Problem.The DIM problem is related to parallel resource allocation problems, encoding theory and network routing. It is NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree three. However, its complexity was open for P k -free graphs for any k ≥ 5; P k denotes a chordless path with k vertices and k − 1 edges. We show in this paper that the weighted DIM problem is solvable in linear time for P 7 -free graphs in a robust way. Let G be a simple undirected graph with vertex set V and edge set E. A subset M of E is an induced matching in G if the G-distance of every pair of edges e, e ∈ M, e = e , is at least two, i.e., e ∩ e = ∅ and there is no edge xy ∈ E with x ∈ e and y ∈ e . A subset M ⊆ E is a dominating edge set if every edge e ∈ E \ M shares an endpoint with some edge e ∈ M, i.e., if e ∩ e = ∅. A dominating induced matching (d.i.m. for short) is an induced matching which is also a dominating edge set.. Let us say that an edge e ∈ E is matched by M if e ∈ M or there is an e ∈ M with e ∩ e = ∅. Thus, M is a d.i.m. of G if and only if every edge of G is matched by M but no edge is matched twice.. The Dominating Induced Matching Problem (DIM, for short) asks whether a given graph has a dominating induced matching. This can also be seen as a special 3-colorability problem, namely the partition into three independent vertex sets A, B, and C such that G[B ∪ C] is an induced matching: If M ⊆ E is a d.i.m. of G then the vertex set has the partition V = A ∪ V (M) with independent vertex set A, and independent sets B, C with B ∪ C = V (M).. Dominating induced matchings are also called edge packings in some papers, and DIM is known as the Efficient Edge Domination Problem (EED for short). A brief history of EED as well as some applications in the fields of resource allocation, encoding theory and network routing are presented in [14] and [16] .. Grinstead et al. [14] showed that EED is NP-complete in general. EED remains hard for bipartite graphs [18] . In particular, [17] shows the intractability of EED for planar bipartite graphs and [10] for very restricted bipartite graphs with maximum degree 3 (the restrictions are some forbidden subgraphs). In [4] , it is shown that the problem remains NP-complete for planar bipartite graphs with maximum degree 3 but is solvable in polynomial time for hole-free graphs (in [9, 17] , the complexity of EED was mentioned as an open problem for weakly chordal graphs which are a subclass of hole-free graphs). Some other new results for EED are given in [7] . In [9] , as another open problem, it is mentioned that for any k ≥ 5, the complexity of DIM is unknown for the class of P k -free graphs. Note that the complexity of the related problems Maximum Independent Set and Maximum Induced Matching is unknown for P 5 -free graphs, and a lot of work has been done on subclasses of P 5 -free graphs.. In this paper, we show that for P 7 -free graphs, DIM is solvable in linear time. Actually, we consider the edge-weighted optimization version of DIM, namely the Minimum Dominating Induced Matching Problem (MDIM), which asks for a dominating induced matching M in G = (V , E) of minimum weight with respect to some given weight function ω : E → R (if existent). For P 5 -free graphs, DIM is solvable in time O(n 2 ) as a consequence of the fact that the clique-width of (P 5 ,gem)-free graphs is bounded [5, 6] and a clique-width expression can be constructed in time O(n 2 ) [3] . In [9] , it is mentioned that DIM is expressible in a certain kind of Monadic Second Order Logic, and in [12] , it was shown that such problems can be solved in linear time on any class of bounded clique-width assuming that the clique-width expressions are given or can be determined in the same time bound. It is well known that the clique-width of cographs (i.e., P 4 -free graphs) is at most 2 (and such cliquewidth expressions can be determined in linear time) and thus the DIM problem can be solved in linear time on cographs. In Sect. 4 we give a simple characterization of cographs having a d.i.m.. Our algorithm for P 7 -free graphs is based on a structural analysis of such graphs having a d.i.m. It is robust in the sense of [20] since it is not required that the input graph is P 7 -free; our algorithm either determines an optimal d.i.m. correctly or finds out that G has no d.i.m. or is not P 7 -free.. The paper is structured as follows: In Sect. 2, we give further basic notions. In Sect. 3, we develop some tools for the main algorithm, in Sect. 4 we solve the DIM problem for cographs in a simple way in linear time, in Sect. 5 we describe structural properties of a P 7 -free graph with d.i.m. and in particular discuss its distance levels with respect to an edge in a d.i.m. In Sect. 6, in procedure Check(xy), for a candidate edge xy (for which it is still unknown whether it is in a d.i.m.), it is analyzed whether its distance levels fulfill the properties of the distance levels described in Sect. 5, and one either obtains a d.i.m. or the answer that the input graph has no d.i.m. or is not P 7 -free. In Sect. 7, as another preparing step, we solve the DIM problem for P 7 -free bipartite graphs in linear time, and finally, in Sect. 8 we solve the DIM problem for P 7 -free graphs robustly in linear time. If one only aims for a polynomial time algorithm then one can carry out Check(xy) for every edge xy in G; most of the tools are only necessary for obtaining a linear time algorithm. In particular, Check(xy) is done only for a fixed number of candidate edges. In this paper we solve the DIM problem in linear time for P 7 -free graphs which answers an open question from [9] . Actually, we solve the minimum weight DIM problem in a robust way in the sense of [20] : Our algorithm either solves the problem correctly or finds out that the input graph has no d.i.m. or is not P 7 -free. This avoids to recognize whether the input graph is P 7 -free; the known recognition time bound is much worse than linear time. It is a challenging open question whether for some k, the DIM problem is NP-complete for P k -free graphs.

O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O