A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical method provides a time-space accuracy control of the solution, and thus, an effective accurate resolution independent of the fastest physical time scale. An important improvement of the computational efficiency is achieved whenever the required time steps go beyond standard stability constraints associated with mesh size or source time scales for the resolution of the drift-diffusion equations, whereas the stability constraint related to the dielectric relaxation time scale is respected but with a second order precision. Numerical illustrations show that the strategy can be efficiently applied to simulate the propagation of highly nonlinear ionizing waves as streamer discharges, as well as highly multi-scale nanosecond repetitively pulsed discharges, describing consistently a broad spectrum of space and time scales as well as different physical scenarios for consecutive discharge/post-discharge phases, out of reach of standard non-adaptive methods. In recent years, plasma discharges at atmospheric pressure have been studied for an increasing list of applications such as chemical and biological decontamination, aerodynamic flow control and combustion [1, 2] . In all these physical configurations, the discharges take usually the form of thin plasma filaments driven by highly nonlinear ionizing waves, also called streamers. These ionizing waves occur as a consequence of the high electric field induced by the fast variations of the net charge density ahead of an electron avalanche with large amplification. The streamer discharge dynamics are mainly governed by the Courant, the effective ionization and the dielectric relaxation times scales [3] , which are usually of the order of 10 −14 − 10 −12 s, whereas the typical time scale of the discharge propagation in centimeter gaps, is about a few tens of nanoseconds. On the other hand, a large variation of space scales needs also to be taken into account, since the Debye length at atmospheric pressure can be as small as a few micrometers, while the inter-electrode gaps, where discharges propagate, are usually of the order of a few centimeters. As a result, the detailed physics of the discharges reveals an important time-space multi-scale character [4, 5] .. More complex applications include plasma assisted combustion or flow control, for which the enhancement of the gas flow chemistry or momentum transfer during typical time scales of the flow of 10 −4 − 10 −3 s, is due to consecutive discharges generated by high frequency (in the kHz range) sinusoidal or pulsed applied voltages [6, 7] . Therefore, during the post-discharge phases of the order of tens of microseconds, not only the time scales are very different from those of the discharge phases of a few tens of nanoseconds, but a completely different physics is taking place. Then, to the rapid multi-scale configuration during discharges, we have to add other rather slower multi-scale phenomena in the post-discharge, such as recombination of charged species, heavy-species chemistry, diffusion, gas heating and convection. Therefore, it is very challenging to accurately simulate the physics of plasma/flow interactions due to the synergy effects between the consecutive discharge/post-discharge phases.. In most numerical models of streamer discharges, the motion of electrons and ions is governed by drift-diffusion equations coupled with Poisson's equation. Early simulation studies were limited to simplified situations where the streamer is considered as a cylinder of constant radius [8, 9, 10, 11] , in which the charged particle densities are assumed to be constant along the radial extension of the streamer: the 1.5D model approach. In this model, the spatio-temporal evolution of the charged particle densities is solved only along one spatial dimension in the direction of propagation, whereas the electric field is calculated in two dimensions using the so-called disc method, based on a direct integration of analytical results. A 2D model for the electric field is indeed essential to properly calculate the electric field enhancement by the space charge in the streamer head. After the first 2D streamer simulations using the Poisson's equation resolution were performed [12] , many studies have been carried out in 2D [3, 13, 14, 15, 16, 17, 18] and 3D [19, 20, 21, 22] .. Being aware of the complexity of fully coupled resolutions of these modeling equations, a decoupling strategy is usually adopted, which considers an independent and successive numerical resolution of Poisson's equation with a fixed charge distribution, and of the drift-diffusion equations with a fixed electric field during each decoupling time step. These computations might be performed explicitly in time with standard first or even second order schemes [23, 24] . In these cases, the time steps are usually limited for the sake of stability by the various characteristic times scales (Courant, ionization, dielectric relaxation), whereas the accuracy of simulations is assumed to be given by the resolution of the fastest physical time scale. In order to somehow overcome the dielectric relaxation limitation, some semi-implicit approaches were developed [25, 26, 27] , based on a predictive approximation of the space charge ahead in time during the electric field computation, even though the other time scale constraints remain. This gain of stability allows important improvements in terms of computational efficiency but the accuracy of simulations becomes rather difficult to quantify.. Another performing technique to improve the efficiency of simulations considers an asynchronous explicit time integration of the drift-diffusion equations with self-adaptive local time-stepping, for which the local time steps are based either on local dynamic increments of the solution [28, 29] or on local Courant conditions [30] . These techniques are the subject of several studies [31, 32, 33] and are mainly conceived to avoid expensive computations whenever the whole system is unnecessarily advanced in time with a global time step prescribed by the fastest scale. Even though these methods yield efficient strategies, specially in terms of CPU time savings, with stable and flux-conserving time integrations, it is rather difficult to conduct an accuracy control on the resolution of the time dependent equations or on their coupling with the electric field resolution for plasma models.. In this work, a numerical study is conducted in order to build a second order explicit in time decoupling scheme for the resolution of the electric field and the electron and ion densities. A lower order and embedded method is taken into account to dynamically compute the decoupling time steps that guarantee an accurate description with error control of the global physical coupling. At this stage, the only limiting time scale is the dielectric relaxation characteristic time for stability reasons. In a second level, the driftdiffusion equations are solved using a Strang second order operator splitting scheme in order to guarantee the global order of the strategy [34, 35] . This time integration scheme considers high order dedicated methods during each splitting time step, which is dynamically adapted by an error control procedure [36] . In this way, even though there is a global advance in time given by the splitting time step, the latter is determined by the desired accuracy of the global physics, which is not necessarily related to the stability constraints associated with the mesh size or the fastest source time scales as demonstrated 3 in [37] . As a consequence, this technique provides an error control procedure and stands as an alternative way to local stepping schemes to overcome time step limitations related to the reaction, diffusion and convection phenomena. Both the electric field and density resolutions are performed on an adapted mesh obtained by a spatial multiresolution method, based on Harten's pioneering work [38] and further developed in [39] , taking into account the spatial multi-scale features of these phenomena with steep spatial gradients. In particular, some grid adaptation techniques for 2D structured meshes were already used [23, 4, 20] and extensions to 3D have been also proposed [20, 19] for streamer simulations. However, one of the main advantages of the multiresolution approach is that it is based on a wavelet representation technique and an error of the spatial approximation can be then mathematically estimated. Consequently, an effective error control is achieved for both the time and space resolution of the multiscale phenomena under study.. The performance of the method is first evaluated for a propagating streamer problem with the multi-scale features previously discussed, for which the various simulation parameters are studied. Once the physical configuration is settled, a 1.5D streamer model is adopted in order to obtain an electric field resolution strategy based on direct computations and derived from analytical expressions, suitable for adapted finite volume discretizations [40] . In a second step, a more complex physical configuration is considered for the simulation of repetitively pulsed discharges, for which a time-space adaptive method is required to efficiently overcome some highly multi-scale features in order to fully describe the various physical phenomena. In this work, only a 1.5D model is considered but extensions to higher dimensions is straightforward for instance with a Poisson's equation solver for adapted grids as it has been implemented in [23, 4, 20] . However, in this paper we focus on the development and validation of new numerical methods for the resolution of the drift-diffusion equations and its coupling with the electric field computation, which are independent of the dimension of the problem. Numerical illustrations of multidimensional problems with the same time-space adaptive strategy with error control will be the subject of future work.. The paper is organized as follows: in Section 2, we present the physical configuration and the modeling equations. The numerical strategy is presented in Section 3, in which the second order adaptive time integration technique is detailed along with the resolution of drift-diffusion equations and the electric field, as well as the spatial multiresolution adaptive procedure. Numerical illustrations are summarized in Section 4 for two configurations given by single propagating and multi-pulsed discharges. We end with some concluding remarks and prospects on future developments and applications. The present work proposes a new numerical strategy for multi-scale streamer simulations. It is based on an adaptive second order time integration strategy that allows to discriminate time scales-related features of the phenomena, given a required level of accuracy of computations. Compared with a standard procedure for which accuracy is guaranteed by considering time steps of the order of the fastest scale, the control error approach implies on the one hand, an effective accurate resolution independent of the fastest physical time scale, and on the other hand, an important improvement of computational efficiency whenever the required time steps go beyond standard stability constraints. The latter is a direct consequence of the self-adaptive time step strategy for the resolution of the drift-diffusion equations which considers splitting time steps not limited by stability constraints for reaction, diffusion and convection phenomena. So far, the global decoupling time steps are limited by the dielectric relaxation stability constraint but with a second order accuracy. Nevertheless, we have also demonstrated that the decoupling time steps are rather chosen based on an accuracy criterion. Besides, if a technique such as a semi-implicit approach is implemented, the same ideas of the proposed adaptive strategy remain valid.. An adaptive multiresolution technique was also proposed in order to provide error control of the spatial adapted representation. The numerical results have proven a natural coupling between time and space accuracy requirements and how the set of time-space accuracy tolerances tunes the precise description of the overall time-space multi-scale phenomenon. As a consequence, the numerical results for multi-pulsed discharge configurations prove that this kind of multi-scale phenomena, previously out of reach, can be successfully simulated with conventional computing resources by this time-space adaptive strategy. And they also show that a consistent physical description is achieved for a broad spectrum of space and time scales as well as different physical scenarios.. In this work, we focused on a 1.5D model in order to evaluate the numerical performance of the strategy. However, the dimension of the problem will only have an influence on the computational efficiency measurements but not on any space-time accuracy or stability aspects. At this stage of development, the same numerical strategy can be coupled with a multi-dimensional Poisson's equation solver, even for adapted grid configurations as developed recently in [23, 4, 20] . Finally, an important amount of work is still in progress concerning programming features such as data structures, optimized routines and parallelization strategies. On the other hand, numerical analysis of theoretical aspects is also underway to extend and further improve the proposed numerical strategy. These issues constitute particular topics of our current research.

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Implementing operations to navigate semantic star schemas In the last years, lots of work have been devoted to multidimensional modeling, star shape schemas and OLAP operations. However, "drill-across" has not captured as much attention as other operations. This operation allows to change the subject of analysis keeping the same analysis space we were using to analyze another subject. It is assumed that this can be done if both subjects share exactly the same analysis dimensions. In this paper, besides the implementation of an algebraic set of operations on a RDBMS, we are going to show when and how we can change the subject of analysis in the presence of semantic relationships, even if the analysis dimensions do not exactly coincide. This paper presents a set of algebraic operations to navigate multidimensional schemas. Each of these operations can be smoothly translated to SQL. Two operations stand out from the rest, i.e. Drill-across and ChangeBase, whose functionality has no counterpart in other models. They work on semantic relationships between different Stars and were not treated as first class citizens in any other multidimensional model before. ChangeBase operation extends the well known "pivoting" functionality, so that it can be used as a step towards Drill-across. Thus, it is shown how we could drill across not only if "dimension tables" are shared, but also if either Dimensions or Facts are related by different kinds of UML Relationships (i.e. Derivation, Generalization, Association, and Flow ).. In our navigational approach for building cube-queries, conditions in the WHERE clause are not explicitly removed. This allows to keep conditions when rolling-up and drillingacross, which offers the possibility of placing conditions on Levels and Dimensions that do not form the space of the analyzed cube. We assume that unnecessary conditions, links and tables are removed by means of semantic optimization mechanisms. As future work, we plan to study the implementation of such mechanisms, as well as how SQL'99 could improve the implementation of the Relationships. In the last years, lots of work have been devoted to modeling multidimensionality (i.e. [17] , [4] , [11] , [8] , [12] , [7] , [27] , [16] , and [21] ). Each one of these models offers an algebraic set of operations (some of them also offer a calculus). However, none of them offers the translation of the operations to SQL (rather they propose alternatives to SQL and relational algebra). Those models proposing alternatives to SQL argue that RDBMS are not well suited for multidimensional purposes. However, the importance of "Relational OLAP" (ROLAP) tools in the market contradicts that, and outlines the importance of research on improving the usage of SQL to query multidimensional data.. [24] presents an end user oriented algebra of multidimensional operations. Nevertheless, it is neither translated to SQL, nor considers drilling across, nor any kind of semantic relationship. An approach limited to operations over Dimensions is in [14] . In this case SQL is extended to facilitate handling dimensional data. Obviously, since it focuses on Dimensions, "drill-across" is not even mentioned.. Semantic relationships are often underestimated, as we can see in [5] , whose methodology for multidimensional design proposes the transformation of generalizations into aggregations and classes. Some few conceptual models, [26] and [25] , allow the representation of semantic relationships. However, these neither present a set of operations to manipulate data, nor study their usage to drill across. Some models offer a "join" operation that would allow some kind of "drill across". Nevertheless, this operation is far away from end user multidimensional concepts, and the benefits of semantic relationships are not explored in any case.

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Performance analysis of direct N-body algorithms for astrophysical simulations on distributed systems We present a performance analysis of different parallelization schemes for direct codes used in the simulation of astrophysical stellar systems. These codes compute the gravitational interaction among stars in an exact way and have a computational complexity of O(N 2 ). Significant improvement in the performance of direct N -body codes can be obtained by means of general purpose massively parallel supercomputers and of special purpose computers like GRAPE hardware. We compare the performance of parallel algorithms on different architectures including a cluster, a supercomputer and two computational grids. The best performance is obtained in combination with GRAPE-6 hardware but highly distributed computational Grids also appear very promising. The simulation of a globular cluster containing about one million stars, currently one of the most challenging numerical problems in astrophysics, is feasible only in combination with GRAPE hardware or on massively parallel architectures.Index Terms-performance analysis, N -body codes, special purpose devices. Numerical algorithms for solving astrophysical N -body problems have evolved in two main directions in recent years. Approximated models like Fokker-Planck models(e.g. [1] ), gaseous models ( [2] ) and Monte Carlo models ( [3] , [4] ) have been applied to the simulation of globular clusters and galactic nuclei. These models permit to follow the global evolution of large systems along their lifetime but at the expense of moderate accuracy and resolution. On the other hand, direct summation methods have been developed to model the dynamics and evolution of collisional systems like dense star clusters. A proper treatment of relaxation effects and close stellar encounters requires highly accurate computations of a large amount of forces between particles which, at the present time, can only be achieved with direct integrators. Direct methods have O(N 2 ) complexity, as they compute the complete set of inter-particle forces at each step and are therefore limited to smaller particle numbers compared to approximated methods.. Significant improvement in the performance of direct codes can be obtained by means of general purpose parallel computers like Beowulf systems or supercomputers ( [5] ) and of special purpose computers like GRAPE hardware ( [6] ).. Two main classes of algorithms are generally used to parallelize direct summation N -body codes:. A. Gualandris and S. Portegies Zwart are with the Astronomical Institute Anton Pannekoek and the Section Computational Science, University of Amsterdam, the Netherlands. A. Tirado-Ramos is with the Section Computational Science, University of Amsterdam, the Netherlands.. • The copy algorithm. Each computing node has a local copy of the whole system but is assigned a specific subset of N/p particles, where N is the total number of particles and p is the number of processors. At every step each node computes the force exerted on its subset of particles by all the other particles in the system, computes their new positions and velocities, and sends the new data to the other processors for update. • The ring or systolic algorithm. Each computing node is only assigned a subset of N/p particles during the initialization phase. At each step each node computes the mutual partial forces exerted on its local particles and then sends the particle data to the neighbor processor.. After p shifts, all the total forces have been computed and the particles are returned to their original processor which can proceed to compute their trajectories. In this paper we present a performance analysis of the two algorithms on different architectures: a cluster, a supercomputer and a computational grid. We confirm that the performance of the ring algorithm can, in some cases, be significantly improved by the use of non-blocking communication which permits to perform calculation and communication at the same time ( [5] ). Finally, from the hardware point of view, we show how the execution times can be greatly reduced if the force calculation is performed by a special purpose GRAPE pipeline.

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Efficient parallel recognition of cographs In this paper, we establish structural properties for the class of complement reducible graphs or cographs, which enable us to describe efficient parallel algorithms for recognizing cographs and for constructing the cotree of a graph if it is a cograph; if the input graph is not a cograph, both algorithms return an induced P 4 . For a graph on n vertices and m edges, both our cograph recognition and cotree construction algorithms run in O(log 2 n) time and require O((n+m)/ log n) processors on the EREW PRAM model of computation. Our algorithms are motivated by the work of Dahlhaus (Discrete Appl. Math. 57 (1995) 29-44) and take advantage of the optimal O(log n)-time computation of the coconnected components of a general graph (Theory Comput. Systems 37 (2004) 527-546) and of an optimal O(log n)-time parallel algorithm for computing the connected components of a cograph, which we present. Our results improve upon the previously known linear-processor parallel algorithms for the problems (Discrete Appl. Math. 57 (1995) 29-44; J. Algorithms 15 (1993) 284-313): we achieve a better time-processor product using a weaker model of computation and we provide a certificate (an induced P 4 ) whenever our algorithms decide that the input graphs are not cographs. The complement reducible graphs, also known as cographs, are defined as the class of graphs formed from a single vertex under the closure of the operations of union and complementation. More precisely, the class of cographs is defined recursively as follows: In this paper, we have presented parallel algorithms for recognizing cographs and for constructing the cotree of a graph if it is a cograph; if the input graph is not a cograph, the algorithms return an induced P 4 . When applied on a graph on n vertices and m edges, both algorithms run in O(log 2 n) time using O((n + m)/ log n) processors on the EREW PRAM model of computation. Thus, our results improve upon the previously known linearprocessor parallel algorithms for the same problems [10, 12] . Instrumental in our work is an optimal parallel algorithm which computes the connected components of a graph or detects that it contains a P 4 ; this algorithm is interesting in its own right as it provides an optimal parallel connectivity algorithm for cographs and can be extended to yield an optimal connectivity algorithm for graphs with constant diameter.. An interesting open question is whether the class of cographs can be optimally recognized on the EREW PRAM model of computation, i.e., whether there exists an O(log n)-time cograph recognition algorithm which runs on the EREW PRAM model and requires O((n+ m)/ log n) processors. Moreover, since cographs form a proper subclass of permutation graphs, a direction for further research would be to investigate whether a similar technique applies for the purpose of recognizing the class of permutation graphs within the same time-processor bounds.. More general classes of perfect graphs, such as the classes of P 4 -reducible and P 4 -sparse graphs, also admit unique tree representations up to isomorphism [14, 15] . Recently, Lin and Olariu presented parallel recognition and tree construction algorithms for P 4 -sparse graphs [20] ; for an input graph on n vertices and m edges, both the recognition and the tree construction algorithms run in O(log n) time using O((n 2 + nm)/ log n) processors on the EREW PRAM model of computation. Thus, it would be interesting to see whether the approach and algorithmic techniques used in this paper can help develop efficient parallel recognition and tree construction algorithms for these two classes of graphs.

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Describing the emotional states that are expressed in speech To study relations between speech and emotion, it is necessary to have methods of describing emotion. Finding appropriate methods is not straightforward, and there are difficulties associated with the most familiar. The word emotion itself is problematic: a narrow sense is often seen as ''correct'', but it excludes what may be key areas in relation to speech--including states where emotion is present but not full-blown, and related states (e.g., arousal, attitude). Everyday emotion words form a rich descriptive system, but it is intractable because it involves so many categories, and the relationships among them are undefined. Several alternative types of description are available. Emotion-related biological changes are well documented, although reductionist conceptions of them are problematic. Psychology offers descriptive systems based on dimensions such as evaluation (positive or negative) and level of activation, or on logical elements that can be used to define an appraisal of the situation. Adequate descriptive systems need to recognise the importance of both time course and interactions involving multiple emotions and/or deliberate control. From these conceptions of emotion come various tools and techniques for describing particular episodes. Different tools and techniques are appropriate for different purposes. The past few years have seen growing interest in what is generally described as Ôspeech and emotionÕ. As the phrase indicates, the research deals with relationships between two domains. To understand the relationships between them, the developing research area needs access to appropriate ways of describing each one individually. This paper is about the ways of describing emotion that might be useful to research in the area. The task is not routine, because there is no generally accepted methodology for describing emotion. Instead, the literature from related disciplines--primarily psychology and biology--contains a variety of alternative approaches and techniques (Cornelius, 1996) . The alternatives persist because each of them has useful features, but none of them quite captures the whole picture, and there is as yet no truly integrative approach on the horizon.. The net result is that the literature on emotion offers the speech community a range of tools that could potentially relate to its concerns. The exact value of any given tool is rarely obvious, though. Our basic aim in this paper is to promote informed choice by ensuring that the key options are in full view. That includes making it clear that the best known options should not be regarded as automatic choices, because there are substantial problems associated with them.. Beyond that, we argue that it is worthwhile for the speech community to engage actively with the problem of describing emotion, rather than expecting to extract solutions ready-made from other disciplines. The point is not that speech research should isolate itself from other research on emotion, but, rather, that it should consider itself capable of making a distinctive contribution, which can and should be fed back into the mainstream of research on emotion.. The paper divides into three broad parts. The first (Sections 2-4) considers what is to be described, and why. The second (Sections 5 and 6) introduces the conceptual issues associated with key approaches to describing relevant states. The third describes specific techniques arising out of these approaches. It is a truism that the value of a tool depends on the purpose for which it is needed. Descriptions are no exception to the rule, especially when the material to be described has multiple dimensions, and can appear to be structured quite differently from different viewpoints. Emotion appears to be a phenomenon of that kind, and it seems unlikely that a single descriptive system to meet all needs will emerge in the near future.. As should be evident from the discussion above, emotion has many aspects that may shape vocal patterns. It makes sense to explore relations between speech variables and these potentially relevant aspects rather than concentrating exclusively on their relationship to a category system that may pose intractable problems. Work on these different aspects is not mutually exclusive, and they should not be regarded as competing approaches. We turn now to a discussion of a set of tools that may prove useful in understanding speech emotion relationships.. Various ways of describing emotion have been outlined. One possible agenda for the speech community is to set about selecting from the range of possibilities those which relate most directly to speech. However, there is also a more radical possibility, which relates to the recurring theme of attempting to understand how emotion tends to be expressed in everyday interactions.. It seems not unlikely that a typical emotional episode will involve vocal elements related to many or all of the different aspects of emotion that have been considered. Consider, for example, an interaction where one partner expresses anger towards another. One might expect to find a close interlacing of vocal signs related not only to anger itself, but also to emotion-related states including hostility and distress. At peaks of anger, vocal patterns related to physiological changes might be expected. More generally, one might expect to find patterns associated with heightened activation and negative valence, and with attempts to achieve socially acceptable control. An overall assessment of the interaction would depend critically on the distribution and sequence of these elements in time. The outcome would depend not only on the signs themselves, but also on the way that they were detected, overlooked, or misinterpreted by the other party, and on the way he or she categorised the speakerÕs behaviour.. If that is a fair picture, then recovering the emotional content of a speech episode will depend on co-ordinating all the forms of description that have been considered, and understanding their various relationships to speech. It is not likely that that will be technically feasible in the short term, but the attempt to achieve it is a genuinely interesting challenge.

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An Iterated Dynasearch Algorithm for the Single-Machine Total Weighted Tardiness Scheduling Problem T his paper introduces a new neighborhood search technique, called dynasearch, that uses dynamic programming to search an exponential size neighborhood in polynomial time. While traditional local search algorithms make a single move at each iteration, dynasearch allows a series of moves to be performed. The aim is for the lookahead capabilities of dynasearch to prevent the search from being attracted to poor local optima. We evaluate dynasearch by applying it to the problem of scheduling jobs on a single machine to minimize the total weighted tardiness of the jobs. Dynasearch is more effective than traditional first-improve or best-improve descent in our computational tests. Furthermore, this superiority is much greater for starting solutions close to previous local minima. Computational results also show that an iterated dynasearch algorithm in which descents are performed a few random moves away from previous local minima is superior to other known local search procedures for the total weighted tardiness scheduling problem. A descent or iterative improvement algorithm is a simple and practical type of local search method for obtaining near-optimal solutions for a wide variety of NP-hard combinatorial optimization problems. The main idea is to improve a feasible solution by performing a series of transformations or moves. The transformations are normally specified by a neighborhood structure, that defines which solutions can be generated by a single move. Given a feasible solution, the algorithm searches its neighborhood for a better solution. If a better solution exists, then one such solution is selected as the current solution and the search repeats; if there is no better solution, then the algorithm terminates. There are two main types of descent algorithms: first-improve, in which the current solution is replaced with the first better solution found in the neighborhood; and best-improve, in which the current solution is replaced with a best solution in the neighborhood. Subsequently, we refer to firstimprove and best-improve as traditional descent algorithms. By definition, any type of descent algorithm terminates in a local optimum. Furthermore, the quality of the final solution as compared with the global optimum depends on the size and the structure of the neighborhood.. The main handicap of a descent algorithm is its myopic nature: it looks only one single move ahead, and any move can lead to a "bad" solution where the search becomes trapped in a local optimum that may be substantially worse than a global optimum. This is the reason that traditional descent algorithms generally cannot compete with more sophisticated local search methods, such as simulated annealing, tabu search, and genetic algorithms, in terms of solution quality. On the positive side, descent algorithms are generally much faster and easier to implement.. A well-known approach for improving the solution quality of a descent algorithm is to adopt a multistart approach in which several independent runs of descent, each using a different randomly generated starting solution, are performed, and then the best of the resulting solutions is selected. However, a far more effective approach is to allow dependent runs by generating the new starting solution from one of the previous local optima by a suitable perturbation method. Such an approach is known as iterated descent, and is a widely-recognized method of obtaining high solution quality at relatively low computational cost, without resorting to more intricate local search algorithms. To stress the power of this type of approach, we note that the iterated Lin-Kernighan algorithm, as implemented by Applegate et al. (1999) , is a state-of-the-art local search algorithm for the traveling salesman problem-and this problem provides the single most competitive stage for testing new local search algorithms.. In this paper, we introduce dynasearch as a new approach for overcoming the myopic nature of traditional descent algorithms. In traditional descent, lexicographic search is used to find either a better or a best solution in a neighborhood that is usually of polynomial size. On the other hand, dynasearch uses dynamic programming in a local search algorithm, so that a neighborhood of exponential size is explored in polynomial time. Specifically, the generic key idea of dynasearch is to consider a neighborhood of the type used in a traditional descent algorithm, but to allow several moves of a certain type to be made in a single iteration. Dynamic programming is used to find the best combination of moves. Thus, each neighbor in a dynasearch algorithm corresponds to one or more moves in traditional descent.. Algorithms that explore exponential neighborhoods in polynomial time have been known for many years, tracing back to the work by Doroshko (1981a, 1981b) for the traveling salesman problem (TSP). In the TSP, a salesman must perform a tour of shortest length, visiting each of n cities exactly once and then returning to the starting city. For an overview of research on such neighborhoods, we refer to the review of Deȋneko and Woeginger (2000) for the TSP, and to the general survey of Ahuja et al. (1999) which covers various problem areas. From these surveys, the main techniques that are identified for performing a search of an exponential number of solutions in polynomial time are matching (or linear assignment) algorithms, cyclic exchange techniques, and dynamic programming (or shortest path algorithms).. We briefly discuss the previous studies that use dynamic programming to explore a neighborhood of exponential size in polynomial time, since this relates most closely to our work on dynasearch. A pyramidal neighbor for the TSP passes through a subset of cities in the original order, and then the remaining cities in the reverse order. Sarvanov and Doroshko (1981a) and Carlier and Villon (1990) give a dynamic programming algorithm that explores in O n 2 time the pyramidal neighborhood, which has size 2 n . Thus, this neighborhood differs from one comprising multiple moves as used in dynasearch. Balas (1999) and Balas and Simonetti (2001) consider a neighborhood for the TSP in which, for some given k, the sequence of cities can be rearranged subject to the constraint that if one city precedes another by more than k positions in the original sequence, then it must also precedes the other city in the rearranged sequence. A dynamic program finds the best of the k − 1 /e n−1 neighbors in O k 2 2 k n time. Again, this neighborhood is not built from multiple moves. A twisted sequence neighborhood for the TSP allows certain non-overlapping sections of the sequence representing the current tour to be reversed. Congram (2000) shows that the size of this neighborhood is 3 + 2 √ 2 n . Moreover, Deȋneko and Woeginger (2000) provide a dynamic programming algorithm that finds the best twisted sequence neighbor in O n 7 time. The twisted sequence neighborhood contains all multiple 2-opt moves (a 2-opt move replaces two edges of the tour with two new edges) that would be produced by dynasearch. However, the high time complexity to search the twisted sequence neighborhood means that it is only of theoretical interest.. In parallel with our work on dynasearch, Hurink (1999) has developed a neighborhood that employs multiple moves for a problem of scheduling a single machine to minimize the total weighted completion time in which batching decisions have to be made. More precisely, each batch of jobs requires a setup time, and all jobs of the same batch have a common completion time, namely the time at which the batch completes its processing. The solution of this problem is represented by a sequence of jobs, since there is an efficient dynamic programming algorithm to form the batches that minimize the total weighted completion time when the sequence is known. Hurink's neighborhood uses multiple transposes of jobs in the sequence. His computational results indicate that this neighborhood is not particularly effective at exploring the solution space relative to one that removes a job from its current position and inserts it elsewhere. Forming a neighborhood from multiple insert moves appears difficult due to the complex relationship between the sequence and the batches produced by the dynamic programming algorithm.. Thus, existing studies in the literature that use a polynomial-time dynamic programming algorithm to search a neighborhood of exponential size are strictly limited. In this respect, our work offers a novel contribution.. This paper also studies the application of dynasearch to the single-machine total weighted tardiness scheduling problem. This work forms part of a research program to evaluate dynasearch as a technique for generating high-quality solutions to a variety of combinatorial optimization problems. The total weighted tardiness problem is an NP-hard archetypal machine scheduling problem for which many local search algorithms have been developed and tested; for an overview see Anderson et al. (1997) . By showing that an iterated dynasearch algorithm outperforms the state-of-the-art local search algorithms, namely the multi-start tabu search algorithm of Crauwels et al. (1998) , we are able to demonstrate the value of the dynasearch approach.. The organization of the paper is as follows. In Section 2, we give a formal description of the singlemachine total weighted tardiness scheduling problem. Section 3 presents the dynasearch concept for the total weighted tardiness problem: it includes a discussion of the structure of the dynasearch neighborhood, the presentation of a polynomial-time dynamic programming algorithm to find the best solution in this neighborhood, the description of a simple dynasearch algorithm without re-starts, and finally some speedups to reduce the computation time. In Section 4, we present the iterated dynasearch algorithm. Here, we first discuss the general principles of multi-start and iterated local search, and then pay special attention to the concept of restarting the local search close to a local optimum. A detailed description of our iterated dynasearch algorithm follows. Section 5 reports on our computation experience. After discussing the design of our computational experiments, we compare multi-start and iterated versions of dynasearch with the corresponding multi-start and iterated versions of first-improve and best-improve descent. We observe that, although multi-start dynasearch is marginally superior to multi-start descent, the performance of iterated dynasearch clearly dominates that of both iterated descent algorithms. Then, we compare iterated dynasearch with the state-of-theart multi-start tabu search algorithm of Crauwels et al. (1998) , and conclude that iterated dynasearch is significantly better. Finally, some concluding remarks are contained in Section 6. The contribution of this paper is twofold. First, a general contribution is the introduction of a new local search technique known as dynasearch. Through its use of dynamic programming, dynasearch explores a neighborhood of exponential size in polynomial time. Since each dynasearch move corresponds to a series of moves in a traditional local search algorithm, dynasearch has a lookahead capability that is not present in these previous methods.. Dynasearch is applicable to a variety of problems for which solutions are naturally represented as sequences. Congram (2000) reports on dynasearch algorithms for the traveling salesman problem and the linear ordering problem that use multiple 2-opt and 3-opt moves, and multiple insert moves, respectively. For each problem, the overall improvement to the objective function that results from the independent moves is equal to the sum of the improvements from the individual moves. When defining independent moves for a particular problem, the definition of independence should be chosen so that individual improvements sum in this way. When we cannot find a suitable definition of independence that produces individual improvements which can be summed, dynasearch cannot be used. A common feature of the total weighted tardiness scheduling problem, the traveling salesman problem and the linear ordering problem is that each can be solved to optimality by a dynamic programming algorithm, although the algorithms have an exponential number of states. Another way of viewing dynasearch is that these dynamic programs are modified according to the current sequence so that some state transitions are forbidden and some states are merged so that a polynomial number of states remains.. For a given problem type, a variety of neighborhoods can be used a dynasearch. For example, in the total weighted tardiness scheduling problem, independent insert moves (an insert move removes a job from its current position and inserts it elsewhere) can be used instead of independent swap moves. More significantly, the flexibility of the approach allows independent swap and insert moves to be used in combination.. The second contribution relates specifically to the application of dynasearch to the single-machine total weighted tardiness scheduling problem. An iterated dynasearch algorithm for this problem performs significantly better than all other known local search algorithms, including the state-of-the-art tabu search algorithm of Crauwels et al. (1998) , with respect to both solution quality and computation time. The explanation for iterated dynasearch finding better solutions is that, after performing a sufficiently large number of random moves from a local minimum, dynasearch stands a much better chance of descending into a different local minimum than traditional descent algorithms. In this way, iterated dynasearch is able to explore more distinct local minima. This performance is entirely attributable to the much larger size of the dynasearch neighborhood: the dynasearch neighborhood contains an exponential number of solutions, while the traditional descent neighborhood contains only a polynomial number of solutions. One explanation for iterated dynasearch being faster is the use various speedups that sometimes reject a move without a complete evaluation of the total weighted tardiness.. In a recent study that was undertaken in parallel with our work, Stützle et al. (1999) apply an ant colony approach to the total weighted tardiness scheduling problem. Essentially, the ant colony generates sequences of jobs through the use of a priority rule with changing parameters. These sequences form the input into a descent algorithm that uses the swap and insert neighborhoods in combination. Although their solutions are of slightly better quality than the ones obtained with our dynasearch algorithm, this is at the expense of extra computation time. As observed above, it is straightforward to extend dynasearch so that independent swap moves and insert moves are used in combination. A fairer comparison of the ant colony approach would be with such an extended dynasearch algorithm.. This paper provides convincing evidence that iterated dynasearch is a powerful new local search technique for a variety of combinatorial optimization problems. One topic for future research is to characterize the types of problems to which dynasearch can be applied. Another topic is to obtain further empirical evidence on the ability of iterated dynasearch to find high-quality solutions of other combinatorial optimization problems, and on its ability to compete with, or outperform, other local search algorithms for these problems.

O 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 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 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 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 B I 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 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 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 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 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 B I 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 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 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 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


Measuring the knowledge-based economy of China in terms of synergy among technological, organizational, and geographic attributes of firms Abstract Using the possible synergy among geographic, size, and technological distributions of firms in the Orbis database, we find the greatest reduction of uncertainty at the level of the 31 provinces of China, and an additional 18.0 % at the national level. Some of the coastal provinces stand out as expected, but the metropolitan areas of Beijing and Shanghai are (with Tianjin and Chongqing) most pronounced at the next-lower administrative level of (339) prefectures, since these four ''municipalities'' are administratively defined at both levels. Focusing on high-and medium-tech manufacturing, a shift toward Beijing, Shanghai, and Tianjin (near Beijing) is indicated, but the synergy is on average not enhanced. High-and medium-tech manufacturing is less embedded in China than in Western Europe. Knowledge-intensive services ''uncouple'' the knowledge base from the regional economies mostly in Chongqing and Beijing. Unfortunately, the Orbis data is incomplete since it was collected for commercial and not for administrative or governmental purposes. However, we provide a methodology that can be used by others who may have access to higher-quality statistical data for the measurement. Most synergy is generated in the knowledge base of the Chinese economy at the provincial level (administrative level 1), but the national level adds a substantial contribution ([18 %). The level of the prefectures seems much less relevant except in the case of Shanghai, Beijing, Chongqing, and Tianjin as ''municipalities'' that are defined also at the (first) level of the provinces. In general, the synergy is generated above the city level; that is, at the level of regions.. A focus on high-and medium-tech manufacturing shows that the differences in terms of this selection can be between 20 and 30 % for provinces. Tianjin joins Beijing and Shanghai as the ''winners'' when taking this perspective, whereas large industrial regions (such as Guangdong) may be less profiled in terms of high-and medium-tech firms. Decomposition in terms of knowledge-intensive services is based on relatively small sets, but BvD claims that services are also included in Orbis and thus this data suggests that the Chinese economy is more manufacturing than service-oriented. The knowledge-intensive services are geographically located in the administrative centers (and perhaps associated to the government; cf. Perevodchikov et al. 2013) . As noted, the major point for discussion is the data collection by the Bureau van Dijk that fills the Orbis database on the basis of information provided by more than one hundred information suppliers and by its own research. The methods of data-collection are discretionary since the information is controlled by the companies in question. This data, therefore, provides an incomplete sample. However, the selection of journals for example by Thomson-Reuters and Elsevier for their databases (Web of Science and Scopus, respectively) is also not public. Thus, such a state of affairs is more common when using commercial databases for scientometric research.. The main remaining question concerns the extent to which one can expect biases in the data-collection to influence the results. We noted that small-sized enterprises are under-represented in this data, and that self-employed entrepreneurs seem not to be included at all. Consequently, startups are presumably not included. This may bias the results against university-based entrepreneurship that may not be distributed equally across the country. However, the industrialized provinces of China all have a considerable number of universities with potentially industrial activities of graduates. This effect, however, may disfavor the largest metropolitan areas such as Beijing and Shanghai. (Hong Kong is not included in this data.) The synergy indicator is not an output but a structural indicator, although-as notedthe number of firms is also registered in Eq. 2 as the units of analysis. Most governmental (OECD) statistics are (linear) output indicators (e.g., Schaaper 2009 ). For example, we found a report entitled ''High-tech statistics China 2012'' on the website of the National Bureau of Statistics 4 which provides a table (1-7) with ''Gross Industrial Output value of high-tech industries by region'' (in RMB ¥100 million). Not surprisingly, this indicator correlates significantly with our indicator using the first-administrative level of 31 provinces; Spearman's q = 0.867 (p \ 0.01). All distributions over the Chinese provinces are skewed and tend therefore to be correlated.. If we focus within the data only on high-and medium-tech, Spearman's q further increases only marginally to .879. However, the regions indicated as most productive in terms of output are different from the ones signaled by our methods, namely Jangsu and Guangdong. These latter regions are among those with the largest numbers of firms in our set: 62,805 and 44,692 firms, respectively. Zhejiang (50,699 firms in our data), however, is categorized with Beijing, Shanghai, and Shandong in the second group by this report, and with Chongqing among the third category. As against these rankings in terms of size, our indicator is a measure of synergy or resonance among the distributions in three (or more) dimensions. The decomposition in terms of sectors and levels taught us that the four municipalities carry a specific function in the knowledge-based economy that was not anticipated. High-and medium-tech is more concentrated in and around the metropolitan areas of Beijing and Shanghai, but setting this filter does not lead to a higher synergy across the provinces (as we had expected on the basis of previous studies). The roles of Chongqing and Beijing as centers of knowledgeintensive administration are notable. In other words, the design allows us to fine-tune in terms of the three relevant dimensions (technology, geography, and size) as different projections of the three-dimensional data. The quality of this data, however, remains beyond our control. As noted above, mutual information in more than three dimensions-the Triple-Helix indicator to be used here-is a signed information measure (Yeung 2008) , and therefore not a Shannon-information (Krippendorff 2009a, b) . However, this measure is derived in the context of information theory and follows from the Shannon formulas (e.g., Abramson 1963; Ashby 1964; McGill 1954) . According to Shannon (1948) the uncertainty in the relative frequency distribution of a random variable x ( P x p x ) can be defined as H X ¼ À P x p x log 2 p x . Shannon denotes this as probabilistic entropy, which is expressed in bits of information if the number two is used as the base for the logarithm. (When multiplied by the Boltzman constant k B , one obtains thermodynamic entropy and the corresponding dimensionality in Joule/Kelvin. Unlike thermodynamic entropy, probabilistic entropy is dimensionless and therefore yet to be provided with meaning when a system of reference is specified.). Likewise, uncertainty in a two-dimensional probability distribution can be defined as H XY ¼ À P x P y p xy log 2 p xy . In the case of interaction between the two dimensions, the uncertainty is reduced with the mutual information or transmission:. In the case of three potentially interacting dimensions (x, y, and z), the mutual information can be derived (e.g., Abramson, 1963, p. 131 ff.) as:. The interpretation is as follows: association information can be categorized broadly into correlation information and interaction information. A spurious correlation in a third attribute, for example, can reduce the uncertainty between the other two. The correlation information among the attributes in a data set can be interpreted as the total amount of information shared among the attributes. The interaction information can be interpreted as multivariate dependencies among the attributes. Compared with correlation, mutual information can be considered as a parsimonious measure for the association. The multivariate extension to mutual information was first introduced by McGill (1954) as a generalization of Shannon's mutual information. This signed information measure (Yeung 2008, p. 59f.) is similar to the analysis of variance, but uncertainty analysis remains more abstract and does not require assumptions about the metric properties of the variables (Garner and McGill 1956) . Han (1980) developed the concept further; positive and negative interactions were also discussed by Jakulin (2005) , Leydesdorff and Ivanova (in press), Sun and Negishi (2010) , Tsujishita (1995), and Yeung (2008, p. 59 f.) . One of the advantages of entropy statistics is that the values can be fully decomposed. As with the decomposition of probabilistic entropy (Theil 1972, p. 20f.) , mutual information in three dimensions can be decomposed into groups as follows:. Since we will decompose in the geographical dimension, T 0 connotes between-region uncertainty; T G the uncertainty prevailing at a geographical scale G; n G is the number of firms at this geographical scale; and N the total number of firms in the whole set. The between-group uncertainty (T 0 ) can be considered as a measure of the dividedness. A negative value of T 0 indicates an additional synergy at the higher level of national agglomeration among the lower-level geographical units. In the Netherlands, Norway, and Sweden, for example, a surplus was found at the national level; in Germany, this surplus was found at the level of the federal states (Länder). Note that one cannot compare the quantitative values of T 0 across countries-because these values are sample-specific-but one is allowed to compare the dividedness in terms of the positive or negative signs of T 0 and as a percentage of the total synergy for each country. All values of the contribution of subsets to the knowledge-based economy are based on normalization on the total set (that is, n G /N in Eq. 2).

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


Analysis of channel allocation scheme for wireless cellular networks Abstract: Compared to wired networks, the communication bandwidth in the wireless networks is limited. In trying to achieve QoS guaranteed wireless services, efficient utilisation of bandwidth resources becomes a fundamental issue. A number of channel allocation schemes have been proposed to fully utilise the wireless bandwidth, but many of them just proposed the channel allocation scheme without presenting a specific channel allocation model. In this paper, we propose and analyse three different channel allocation schemes for wireless networks. We build three system models based on a two-dimensional Markov chain to compute the performance of base station in terms of the new call blocking probability, the handover dropping probability, and the channel utilisation. Wireless communication technology has gained widespread acceptance in recent years (Lindemann and Thümmler, 2001) . A lot of services which are provided by the wired network have been supported by the wireless equipment. With different network services, the demand for supporting multi-type traffic applications in wireless network has increased dramatically. To achieve QoS guaranteed wireless network service, it is important to provide an effective bandwidth allocation scheme, which not only fully utilises the scarce wireless bandwidth but also minimises the call termination probabilities and call blocking probabilities.. A wireless network is composed of several base stations through which the wireless equipment connects to the network. The radio coverage of each base station is called a cell, just like a Personal Communication System (PCS) (Fang et al., 1997; Lin et al., 1994) . Within each cell, there are mainly two classes of call traffic: new call and handover call. A new call is the one which is generated in the current cell, while a handover call is the one that is generated in another cell but transferred (handed over) into the current cell (Panoutsopoulos and Kotsopoulos, 2002) . When a call enters into the radio coverage of current cell, the channel allocation scheme decides whether the attempt of this call can obtain an available channel or not. If not, the call is dropped immediately. Once a channel has been assigned to a call, the channel will not be released by the call until the call is finished or handed over to another cell. Handover represents the process of changing some radio parameters of the channel (e.g., frequency, time slot, and spreading code) occupied by an existing connection. The handover process is often initiated either by crossing a cell boundary or by a deteriorated quality of received signal on the currently employed channel. For network users, it is better to block a new call attempt than to drop an ongoing call (Tekinay, 1991) . The interruption of an ongoing call should be considered to be more serious than blocking an attempt of a new call. Due to the scarce resources, with more traffic, the residual capacity of the cell's size gets smaller and smaller, which may increase the call handover frequency (Lin et al., 1991) . For example, the IMT-2000 system uses a microcell structure with a diameter of a few hundreds of metres, which incurs more frequent handover and limits the performance of the wireless cellular network (Agrawal and Zeng, 2003) . Therefore, it is important to balance the QoS of base station and the number of mobile devices served. Different handover strategies have been proposed in literature (Tekinay, 1991; Lin et al., 1991; Chiu and Bassioni, 2000; Ortigoza-Guerrero and Aghvami, 1999) . These works assign higher priorities to handover requests with reserved channels and demonstrate that the handover prioritisation schemes are very efficient in improving the QoS of wireless networks. While these previous works focused on how to assign higher priorities to handover call, there is little discussion about how to model the channel allocation process of the base station. Lopez-Mellado models the channel allocation process with a Petri network (Mellado and Molina-Ramirez, 1995) . In Fantacci (2000) , the handover attempts are queued according to the FIFO policy, and the status of the queue is analysed with a simple Markov chain. Since there is little discuss about the reserved channel allocation and there is no efficient metric to evaluate the performance of channel allocation scheme, this paper proposes three channel allocation models for three different channel allocation schemes. A performance metric of Grade of Service (GoS) is introduced to analyse the performance of the base station. The performance of the channel allocation scheme is also analysed with regard to new call blacking probability, handover call dropping probability, and channel utilisation. Meanwhile, an effective method is also provided to find out the optimal number of reserved channels in an iterative way.. The rest of the paper is organised as follows. Section 2 introduces the general channel allocation process and proposes three channel allocation schemes. The analysis of the performance of base station with different channel allocation schemes is presented in Section 3. The method of finding out the optimal number of reserved channel is provided at the end of the section. Some performance results are presented in Section 4. Section 5 concludes the paper and discusses the future research. In this paper, three kinds of channel allocation schemes are discussed: NPC, FSC and FRC. We propose three channel allocation models to analyse the channel allocation process of wireless networks and employ the two-dimensional Markov model to analyse the new call blocking probability, handover call dropping probability, and channel utilisation. The performance metric of GoS is employed to evaluate the three schemes. Extensive numerical results show that the usage of reserved channel can improve the GoS of base station greatly. In order to improve the bandwidth utilisation of the base station, the tradeoff between the number of service channels and the QoS of base station should be addressed. Furthermore, the channel allocation scheme is a critical factor to improve the network's performance and resource utilisations. This probability model is discussed in the circuit switching network, in which each call will hold the channel until the call is finished or handed over to another cell. We are currently investigating whether this model can be adapted to packet switching networks.

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Self-stabilizing byzantine agreement Byzantine agreement algorithms typically assume implicit initial state consistency and synchronization among the correct nodes and then operate in coordinated rounds of information exchange to reach agreement based on the input values. The implicit initial assumptions enable correct nodes to infer about the progression of the algorithm at other nodes from their local state. This paper considers a more severe fault model than permanent Byzantine failures, one in which the system can in addition be subject to severe transient failures that can temporarily throw the system out of its assumption boundaries. When the system eventually returns to behave according to the presumed assumptions it may be in an arbitrary state in which any synchronization among the nodes might be lost, and each node may be at an arbitrary state. We present a self-stabilizing Byzantine agreement algorithm that reaches agreement among the correct nodes in optimal time, by using only the assumption of bounded message transmission delay. In the process of solving the problem, two additional important and challenging building blocks were developed: a unique self-stabilizing protocol for assigning consistent relative times to protocol initialization and a Reliable Broadcast primitive that progresses at the speed of actual message delivery time. The Byzantine agreement (Byzantine Generals) problem was first introduced by Pease, Shostak and Lamport [11] . It is now considered as a fundamental problem in fault-tolerant * Part of the research was done while visiting Cornell University. distributed computing. The task is to reach agreement in a network of n nodes in which up-to f nodes may be faulty. A distinguished node (the General or the initiator ) broadcasts a value m, following which all nodes exchange messages until the non-faulty nodes agree upon the same value. If the initiator is non-faulty then all non-faulty nodes are required to agree on the same value that the initiator sent. Standard deterministic Byzantine agreement algorithms operate in the synchronous network model in which it is assumed that all correct nodes initialize the agreement procedure (and any underlying primitives) at about the same time. By assuming concurrent initializations of the algorithm a synchronous rounds structure can be enforced and used to infer on the progression of the algorithm from the point of initialization. Moreover, there is always an implicit assumption about the consistency of the initial states of all correct nodes, or at least a quorum of them.. We consider a more severe fault-model in which in addition to the permanent presence of Byzantine failures, the system can also be subject to severe transient failures that can temporarily throw all the nodes and the communication subsystem out of the assumption boundaries. E.g. resulting in more than one third of the nodes being Byzantine or messages of non-faulty nodes getting lost or altered. This will render the whole system practically unworkable. Eventually the system must experiences a tolerable level of permanent faults for a sufficiently long period of time. Otherwise it would remain unworkable forever. When the system eventually returns to behave according to the presumed assumptions, each node may be in an arbitrary state. It makes sense to require a system to resume operation after such a major failure without the need for an outside intervention to restart the whole system from scratch or to correct it.. Classic Byzantine algorithms cannot guarantee to execute from an arbitrary state, because they are not designed with self-stabilization in mind. They typically make use of assumptions on the initial state of the system such as assuming all clocks are initially synchronized or that the initial states are initialized consistently at all correct nodes (cf. from the very first polynomial solution [8] through many others like [12] ). Conversely, A self-stabilizing protocol converges to its goal from any state once the system behaves well again, but is typically not resilient to the permanent presence of faults.. In trying to combine both fault models, Byzantine failures present a special challenge for designing self-stabilizing distributed algorithms due to the "ambition" of malicious nodes to incessantly hamper stabilization. This difficulty may be indicated by the remarkably few algorithms resilient to both fault models (see [4] for a review). The few published selfstabilizing Byzantine algorithms are typically complicated and sometimes converge from an arbitrary initial state only after exponential or super exponential time ( [7] ).. In our model correct nodes cannot assume a common reference to time or even to any common anchor in time and they cannot assume that any procedure or primitive initialize concurrently. This is the result of the possible loss of synchronization following transient faults that might corrupt any agreement or coordination among the correct nodes and alter their internal states. Thus synchronization must be restored from an arbitrary state while facing on-going Byzantine failures. This is a very tricky task considering that all current tools for containing Byzantine failures, such as [2, 12] , assume that synchronization already exists and are thus preempted for use. Our protocol achieves self-stabilizing Byzantine agreement without the assumption of any existing synchrony besides bounded message delivery. In [1] it is proven to be impossible to combine self-stabilization with even crash faults without the assumption of bounded message delivery.. Note that the problem is not relaxed even in the case of a one-shot agreement, i.e. in case that it is known that the General will initiate agreement only once throughout the life of the system. Even if the General is correct and even if agreement is initiated after the system has returned to its coherent behavior following transient failures, then the correct nodes might hold corrupted variable values that might prevent the possibility to reach agreement. The nodes have no knowledge as to when the system returns to coherent behavior or when the General will initiate agreement and thus cannot target to reset their memory exactly at this critical time period. Recurrent agreement initialization by the General allows for recurrent reset of memory with the assumption that eventually all correct nodes reset their memory in a coherent state of the system and before the General initializes agreement. This introduces the problem of how nodes can know when to reset their memory in case of many ongoing concurrent invocations of the algorithm, such as in the case of a faulty General disseminating several values all the time. In such a case correct nodes might hold different sets of messages that were sent by other correct nodes as they might reset their memory at different times.. In our protocol, once the system complies with the theoretically required bound of 3f < n permanent Byzantine faulty nodes in a network of n nodes and messages are delivered within bounded time, following a period of transient failures, then regardless of the state of the system, the goal of Byzantine agreement is satisfied within O(f ′ ) communication rounds (where f ′ ≤ f is the actual number of concurrent faults). The protocol can be executed in a one-shot mode by a single General or by recurrent agreement initializations and by different Generals. It tolerates transient failures and permanent Byzantine faults and makes no assumption on any initial synchronized activity among the nodes (such as having a common reference to time or a common event for triggering initialization).. For ease of following the arguments and proofs, the structure and logic of our ss-Byz-Agree procedure is modeled on that of [12] . The rounds in that protocol progress following elapsed time. Each round spans a constant predefined time interval. Our protocol, besides being self-stabilizing, has the additional advantage of having a message-driven rounds structure and not time-driven rounds structure. Thus the actual time for terminating the protocol depends on the actual communication network speed and not on the worst possible bound on message delivery time.. It is important to note that we have previously presented a distributed self-stabilizing Byzantine pulse synchronization procedure in [3] . It aims at delivering a common anchor in time to all correct nodes within a short time following transient failures and with the permanent presence of Byzantine nodes. We have also previously presented a protocol for making any Byzantine algorithm be self-stabilizing [5] , assuming the existence of synchronized pulses. Byzantine agreement can easily be achieved using a pulse synchronization procedure: the pulse invocation can serve as the initialization event for round zero of the agreement protocol. Thus any existing Byzantine agreement protocol may be used, on top of the pulse synchronization procedure, to attain self-stabilizing Byzantine agreement. The current paper achieves Byzantine agreement without assuming synchronized pulses. Moreover, we show in [6] that synchronized pulses can actually be produced more efficiently atop the protocol in the current paper. This pulse synchronization procedure can in turn be used as the pulse synchronization mechanism for making any Byzantine algorithm selfstabilize, in a more efficient way and in a more general model than by using the pulse synchronization procedure in [3] .. In [13] it is shown how to initialize Byzantine clock synchronization without assuming a common initialization phase. It can eventually also execute synchronized Byzantine agreement by using the synchronized clocks. The solution is not self-stabilizing as nodes are booted and thus do not initialize with arbitrary values in the memory.. In [9] consensus is reached assuming eventual synchrony. Following an unstable period with unbounded failures and message delays, eventually no node fails and messages are delivered within bounded, say d, time. At this point there is no synchrony among the correct nodes and they might hold copies of obsolete messages. This is seemingly similar to our model but the solution is not truly self-stabilizing since the nodes do not initialize with arbitrary values. Furthermore, the solution only tolerates stopping failures and no new nodes fail subsequent to stabilization. Consensus is reached within O(d). That paper also argues that in their model, although with Byzantine failures, consensus cannot be reached within less than O(f ′ )·d time, which is essentially identical to our time complexity. Our solution operates in a more severe fault model and thus converges in optimal time.

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