uncorrelated random networks we define a statistical ensemble of nondegenerate graphs i e graphs without multiple connections and self connections between nodes the node degree distribution is arbitrary but the nodes are assumed to be uncorrelated this completes our earlier publication phys rev 64 046118 2001 where trees and degenerate graphs were considered an efficient algorithm generating nondegenerate graphs is constructed the corresponding computer code is available on request finite size effects in scale free graphs i e those where the tail of the degree distribution falls like n beta are carefully studied we find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like n gamma with gamma min 1 2 1 beta 1 where n is the total number of nodes the consequence is that independently of any specific model the internode correlations seem to be a necessary ingredient of the physics of scale free networks observed in nature

a comparison of discrete algorithms for fuzzy weighted average fuzzy weighted average fwa which can be applied to various fields such as engineering design decision analysis etc and as function of fuzzy numbers is suitable for the problem of multiple occurrences of fuzzy parameters additional fuzziness may be introduced in the alpha cut arithmetic this paper reviews and compares discrete algorithms for the fwas in both theoretical comparison and numerical comparisons as opposed to the linear programming algorithms that may be efficient but require the help of linear programming software an alternative efficient algorithm is also proposed the algorithm introduces an all candidate criteria ratings weights replaced benchmark adjusting procedure other than a binary dichotomy search in the existing methods the theoretical worst case comparison shows that the algorithms of guu and guh and our alternative algorithm require the same order of calculation complexity o n where n is the number of fwa terms yet the guh algorithm always requires 2 n 1 calculations to be performed the algorithm of guu requires the elemental comparison complexity o n and is superior to the other algorithms in the worst case on the other hand our alternative algorithm and lee and park algorithm have the same comparison complexity o n log n yet our alternative algorithm requires o n calculation complexity which is better than o n log n of the lee and park algorithm the numerical experiments show that the algorithm of guu and our alternative algorithm generally perform and converge faster by requiring fewer calculations than that of lee and park s algorithm the alternative algorithm requires a slightly smaller number of calculations than that of the guu algorithm due to the use of the convergent benchmark adjustment procedure rather than a somewhat fixed binary search conversely in the number of element comparisons lee and park s algorithm is shown numerically generally slightly better than the alternative algorithm due to the simple binary search scheme used the alternative algorithm also requires fewer comparisons than that of the guu algorithm furthermore in comparison of the average cpu time requirements the ranks of the results of these algorithms are consistent with those of the algorithms for the average numbers of calculations in general the alternative algorithm may provide an efficient alternative algorithm to the fwas in the worse case situation the guu algorithm still may be considered as an efficient alternative

emulation of utility functions over a set of permutations sequencing reliability growth tasks abstractwe consider bayesian design of experiments problems in which we maximise the prior expectation of a utility function over a set of permutations for example when sequencing a number of tasks to perform when the number of tasks is large and the expected utility is expensive to compute it may be unreasonable or infeasible to evaluate the expected utility of all permutations we propose an approach to emulate the expected utility using a surrogate function based on a parametric probabilistic model for permutations the surrogate function is fitted by maximising the correlation with the expected utility over a set of training points we propose a suitable transformation of the expected utility to improve the fit we provide results linking the correlation between the two functions and the number of expected utility evaluations to undertake the approach is applied to the sequencing of reliability growth tasks in the development of hardware systems in which there is a large number of potential tasks

global convergence of karnik mendel algorithms karnik mendel km algorithms are the most commonly used iterative type reduction methods in interval type 2 fuzzy sets and systems as well as new techniques for computing the fuzzy weighted average fwa various extensions and improvements have been proposed however no proof has been provided for the convergence of these extensions it is necessary to provide the proof because many of the iterative algorithms may have divergence cases in the present study we provide a theoretical proof that km algorithms exhibit global convergence different initialization methods and iteration formats can always obtain the same unique optimal solution thus there are no concerns about the possibility of divergence in extensions of km algorithms our proof provides theoretical support for the applications of km algorithms especially the type reduction designs used in type 2 fuzzy systems and fwa computations because of the important roles of km algorithms in these methods

a hybrid dynamic programming branch and bound algorithm for the multiple choice knapsack problem abstract dynamic programming and branch and bound methodologies are combined to produce a hybrid algorithm for the multiple choice knapsack problem lagrangian duality is used in a computationally efficient manner to compute tight bounds on every active node in the search tree the use of lagrangian duality also enables the use of a reduction procedure to reduce the size of the problem for the enumeration phase computational experience with up to 200 multiple choice sets and 20000 zero one variables is reported the computational experience indicates that the resulting algorithm is faster than the best published algorithm and is simpler to code

the fuzzy weighted average within a generalized means function the fuzzy weighted average is widely used to solve hierarchical evaluation problems including fuzzy consideration for the operations of scoring weighting and aggregating previous works considered the fuzziness of score and weight and used the additive function to aggregate these weighted scores this study considers the aggregation operator also as a fuzzy variable and uses a generalized means function to fuzzify the aggregation operator within a fuzzy weighted average in practice the proposed model not only considers both the relative important of the criteria and its achieved performance but also conveys the influence of the dm s decision maker s evaluation attitude thus the proposed model can flexibly reflect any dm s evaluation attitude such as open neutral or rigorous thereby the proposed model can make an objective evaluation that approaches a real decision making situation and thus has the potential to be a useful management tool for improved resolution of fuzzy hierarchical evaluation problems

detection of topological patterns in complex networks correlation profile of the internet abstract a general scheme for detecting and analyzing topological patterns in large complex networks is presented in this scheme the network in question is compared with its properly randomized version that preserves some of its low level topological properties statistically significant deviation of any topological property of a network from this null model likely reflects its design principles and or evolutionary history we illustrate this basic scheme using the example of the correlation profile of the internet quantifying correlations between degrees of its neighboring nodes this profile distinguishes the internet from previously studied molecular networks with a similar scale free degree distribution we finally demonstrate that the clustering in a network is very sensitive to both the degree distribution and its correlation profile and compare the clustering in the internet to the appropriate null model

overview of metrics and their correlation patterns for multiple metric topology analysis on heterogeneous graph ensembles this study is an overview of network topology metrics and a computational approach to analyzing graph topology via multiple metric analysis on graph ensembles the paper cautions against studying single metrics or combining disparate graph ensembles from different domains to extract global patterns this is because there often exists considerable diversity among graphs that share any given topology metric patterns vary depending on the underlying graph construction model and many real data sets are not actual statistical ensembles as real data examples we present five airline ensembles comprising temporal snapshots of networks of similar topology wikipedia language networks are shown as an example of a nontemporal ensemble general patterns in metric correlations as well as exceptions are discussed by representing the data sets via hierarchically clustered correlation heat maps most topology metrics are not independent and their correlation patterns vary across ensembles in general density related metrics and graph distance based metrics cluster and the two groups are orthogonal to each other metrics based on degree degree correlations have the highest variance across ensembles and cluster the different data sets on par with principal component analysis namely the degree correlation the s metric their elasticities and the rich club moments appear to be most useful in distinguishing topologies

organization of complex networks without multiple connections we find a new structural feature of equilibrium complex random networks without multiple and self connections we show that if the number of connections is sufficiently high these networks contain a core of highly interconnected vertices the number of vertices in this core varies in the range between const x n1 2 and const x n2 3 where is the number of vertices in a network at the birth point of the core we obtain the size dependent cutoff of the distribution of the number of connections and find that its position differs from earlier estimates

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

an exact algorithm for the reliability redundancy allocation problem abstract the redundancy allocation problem is the problem of finding an optimal allocation of redundant components subject to a set of resource constraints the problem studied in this paper refers to a series parallel system configuration and allows for component mixing we propose a new modeling solution approach in which the problem is transformed into a multiple choice knapsack problem and solved to optimality via a branch and cut algorithm the algorithm is tested on well known sets of benchmark instances all instances have been solved to optimality in milliseconds or very few seconds on a normal workstation

fractional programming approach to fuzzy weighted average this paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average based on the cut representation of fuzzy sets and the extension principle a pair of fractional programs is formulated to find the cut of fuzzy weighted average owing to the special structure of the fractional programs in most cases the optimal solution can be found analytically consequently the exact form of the membership function can be derived by taking the inverse function of the cut for other cases a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method examples are given for illustration

clustering of correlated networks we obtain the clustering coefficient the degree dependent local clustering and the mean clustering of networks with arbitrary correlations between the degrees of the nearest neighbor vertices the resulting formulas allow one to determine the nature of the clustering of a network

generation of uncorrelated random scale free networks uncorrelated random scale free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks we propose and analyze a model capable of generating random uncorrelated scale free networks with no multiple and self connections the model is based on the classical configuration model with an additional restriction on the maximum possible degree of the vertices we check numerically that the proposed model indeed generates scale free networks with no two and three vertex correlations as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k respectively complex networks constitute a general framework for the topological characterization of many natural and technological systems whose complexity prevents a more detailed microscopic description f1 3g within this framework these systems are represented in terms of networks or graphs f4g in which vertices stand for the units composing the system while edges among vertices represent the interactions or relations between pairs of units the focus is thus shift to the topological characterization of the representative network a task which is largely more feasible and yields nevertheless a noticeable amount of information on the structure and properties of the original system the empirical analysis of many real complex networks has unveiled the presence of several typical properties widely found in systems belonging to a large variety of realms one of the most relevant is given by the scale free nature of the degree distribution pskd f1 3 5g defined as the probability that a randomly chosen vertex has degree k si e it is connected to other k verticesd in mathematical terms the scale free property translates into a power law function of the form psk d k g

simplified type 2 fuzzy sliding controller for wing rock system wing rock is a highly nonlinear phenomenon in which aircrafts with slender delta wings undergo limit cycle roll oscillations at high angles of attack a simplified type 2 fuzzy sliding controller is designed for suppressing wing rock phenomena and tracking the desired trajectories to reduce the computational complexity of a type reducer the end points of a type reduced set are approximated by the outputs of two standard fuzzy sliding mechanisms in the proposed simplified type 2 fuzzy sliding controller furthermore the sliding modes of the fuzzy sliding control system are guaranteed simulation results are included to show the effectiveness of the proposed simplified type 2 fuzzy sliding controller

reliability redundancy allocation an improved realization for nonconvex nonlinear programming problems the redundancy allocation problem which seeks to find the optimal allocation of redundancy that maximizes system reliability is one of the representative problems in reliability optimization the problem can be formulated as a nonconvex integer nonlinear programming problem this paper presents an efficient branch and bound approach to solve this problem where the considered system is coherent that is the objective and constraint functions have monotonic increasing properties the proposed method is based primarily on a search space elimination of disjoint sets in a solution space that does not require any relaxation of branched subproblems the main advantage of the proposed method is flexibility i e it does not rely on any assumptions of linearity separability single constraint or convexity which make the method adaptive to various applications numerical experiments demonstrate that the method is superior to the existing exact algorithms for redundancy allocation problems in terms of computation time

spectra of real world graphs beyond the semicircle law results on the spectra of adjacency matrices corresponding to models of real world graphs we find that when the number of links grows as the number of nodes the spectral density of uncorrelated random matrices does not converge to the semicircle law furthermore the spectra of real world graphs have specific features depending on the details of the corresponding models in particular scale free graphs develop a trianglelike spectral density with a power law tail while small world graphs have a complex spectral density consisting of several sharp peaks these and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks

observability transitions in correlated networks yang wang and motter phys rev lett 109 258701 2012 analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable the size of the connected components comprising the observable nodes is a major concern of the model we analyze this model in random heterogeneous networks with degree correlation with numerical simulations and analytical arguments based on generating functions we find that negative degree correlation makes networks more observable this result holds true both when the sensors are placed on nodes one by one in a random order and when hubs preferentially receive the sensors finally we numerically optimize networks with a fixed degree sequence with respect to the size of the largest observable component optimized networks have negative degree correlation induced by the resulting hub repulsive structure the largest hubs are rarely connected to each other in contrast to the rich club phenomenon of networks

asymptotic properties of degree correlated scale free networks the possible correlation profiles of networks with a given scale free degree distribution are restricted and bounded by maximally correlated configurations dissortative networks consist of nested bilayers in which low degree vertices are connected to high degree vertices the number of these bilayers attains a constant value for large network size n assortative networks exhibit monolayers of low degree vertices the number of which grows monotonously with n analytical relations for the pearson correlation coefficient r of these extremal configurations are derived and shown to provide lower and upper bounds on the possible r values both bounds are found to vanish for large networks

fuzzy weighted average an improved algorithm abstract this paper suggests a modification on the fuzzy weighted average fwa method developed by dong and wong 1987 a steepest descend ascend method is proposed to facilitate steps 3 and 4 of the fwa to find the minimum maximum of f x1 x2 xn w1 w2 wn i 1n wixi i 1n wi an example used by dong and wong is again employed to illustrate the new method the same results are obtained but the new method requires much less evaluations and computations the advantages and disadvantages of the two algorithms are discussed also several relevant theorems are stated and discussed in this paper and the proofs of these theorems are listed in the appendix

the computation of the worst conditional expectation abstract recent advances in risk theory identify risk as a measure related to the tail of a probability distribution function since it represents the worst outcomes of the random variable measures like value at risk var conditional var expected shortfall and so on have become familiar operational tools for many financial applications in this paper one of these measures the worst conditional expectation with threshold of a discrete random variable z shortly wce z is considered it has been found that its computation can be formulated as a fractional integer programming problem with a single linear constraint but its complexity is np hard therefore it must be solved by implicit enumeration due to its similarity with the knapsack problem it has been found that a good upper bound and a sharp data structure allow the implementation of a branch bound that is able to solve realistic size problems in less than one hundredth of a second

aggregation using the linguistic weighted average and interval type 2 fuzzy sets the focus of this paper is the linguistic weighted average lwa where the weights are always words modeled as interval type 2 fuzzy sets it2 fss and the attributes may also but do not have to be words modeled as it2 fss consequently the output of the lwa is an it2 fs the lwa can be viewed as a generalization of the fuzzy weighted average fwa where the type 1 fuzzy inputs are replaced by it2 fss this paper presents the theory algorithms and an application of the lwa it is shown that finding the lwa can be decomposed into finding two fwas since the lwa can model more uncertainties it should have wide applications in distributed and hierarchical decision making

diversity of graphs with highly variable connectivity a popular approach for describing the structure of many complex networks focuses on graph theoretic properties that characterize their large scale connectivity while it is generally recognized that such descriptions based on aggregate statistics do not uniquely characterize a particular graph and also that many such statistical features are interdependent the relationship between competing descriptions is not entirely understood this paper lends perspective on this problem by showing how the degree sequence and other constraints e g connectedness no self loops or parallel edges on a particular graph play a primary role in dictating many features including its correlation structure building on recent work we show how a simple structural metric characterizes key differences between graphs having the same degree sequence more broadly we show how the often implicit choice of a background set against which to measure graph features has serious implications for the interpretation and comparability of graph theoretic descriptions

enhanced karnik mendel algorithms the karnik mendel km algorithms are iterative procedures widely used in fuzzy logic theory they are known to converge monotonically and superexponentially fast however several usually two to six iterations are still needed before convergence occurs methods to reduce their computational cost are proposed in this paper extensive simulations show that on average the enhanced km algorithms can save about two iterations which corresponds to more than a 39 reduction in computation time an additional at least 23 computational cost can be saved if no sorting of the inputs is needed

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

fuzzy weighted averages revisited the fuzzy weighted average operations are common operations in risk and decision analysis based on zadeh s extension principle dong and wang fuzzy sets and systems 21 1987 183 proposed a fwa method a method based on the cut representation of fuzzy sets and interval analysis the fwa method provides a discrete approximation of the cuts of fuzzy weighted average the fwa method has an exponential complexity subsequently liou and wang fuzzy sets and systems 49 1992 307 proved that indeed the fwa method can be simplified to be a nonconstrainted linear fractional programming problem with lower and upper bounds for each of the variables they proposed an improved algorithm called ifwa which is of o n2 complexity where n is the number of decision variables in ifwa guh et al comput math appl 32 8 1996 115 proposed a max min paired elimination method pfwa they claimed their pfwa was of order n in complexity yet the pfwa is a heuristic method lacking any proof of convergence in 1997 lee and park proposed an algorithm efwa which is of o nlogn complexity most recently kao and liu fuzzy sets and systems 120 2001 435 solved the fwa by transforming the fractional program into a linear program in this note we shall relate the ifwa framework with the nonconstrainted 0 1 integer linear fractional programming problem in the mathematical programming literature several o n time algorithms have been existing for instance robillard naval res logist quart 18 1971 47 and hansen et al math programming 52 1991 255 the algorithm of hansen et al will be presented for easy reference

hyperbolic set covering problems with competing ground set elements motivated by a challenging problem arising in wireless network design we investigate a new nonlinear variant of the set covering problem with hyperbolic objective function each ground set element user competes with all its neighbors interfering users for a shared resource the network access time and the goal is to maximize the sum of the resource share assigned to each ground set element the network efficiency while covering all of them the hyperbolic objective function privileges covers with limited overlaps among selected subsets in a sense this variant lies in between the set partitioning problem where overlaps are forbidden and the standard set covering problem where overlaps are not an issue at all we study the complexity and approximability of generic and euclidean versions of the problem present an efficient lagrangean relaxation approach to tackle medium to large scale instances and compare the computational results with those obtained by linearizations

reshuffling scale free networks from random to assortative to analyze the role of assortativity in networks we introduce an algorithm which produces assortative mixing to a desired degree this degree is governed by one parameter p changing this parameter one can construct networks ranging from fully random p 0 to totally assortative p 1 we apply the algorithm to a barabasi albert scale free network and show that the degree of assortativity is an important parameter governing the geometrical and transport properties of networks thus the average path length of the network increases dramatically with the degree of assortativity moreover the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different the behavior of the clustering coefficient is also discussed

hyperbolic 0 1 programming and query optimization in information retrieval unconstrained hyperbolic 0 1 programming can be solved in linear time when the numerator and the denominator are linear and the latter is always positive it is np hard and finding an approximate solution with a value equal to a positive multiple of the optimal one is also np hard if this last hypothesis does not hold determining the optimal logical form of a query in information retrieval given the attributes to be used can be expressed as a parametric hyperbolic 0 1 program and solved in o n logn time wheren is the number of elementary logical conjunctions of the attributes this allows to characterize the optimal queries for the van rijsbergen synthetic criterion

analytical solution methods for the fuzzy weighted average for the fuzzy weighted average fwa despite various discrete solution algorithms and their improvements attempts at analytical solutions are very rare this paper provides an analytical solution method for the fwa based on the conclusions of the karnik mendel km algorithm compared with the two current popular kinds of a cut based computational methods for the fwa mathematical programming transformations and direct iterate computations our method is precise and has a concise structure efficient computation process and sound theoretical proofs we propose two algorithms for computing the analytical solution of the fwa two numerical examples illustrate our proposed approach

an efficient algorithm for fuzzy weighted average in multisensor intelligent systems the information fusion plays an important role several algorithms have been proposed for the purpose of aggregating imprecise sensory information represented by fuzzy numbers this paper proposes an efficient algorithm to compute fuzzy weighted average which turned out to be superior to the previous works by reducing the number of comparisons and arithmetic operations to o n log n

study on enhanced karnik mendel algorithms initialization explanations and computation improvements computing the centroid of an interval type 2 fuzzy set is an important operation in a type 2 fuzzy logic system and is usually implemented by karnik mendel km iterative algorithms by connecting km algorithms and continuous km algorithms together this paper gives theoretical explanations on the initialization methods of km and enhanced karnik mendel ekm algorithms proposes exact methods for centroid computation of an interval type 2 fuzzy set and extends the enhanced karnik mendel ekm algorithms to three different forms of weighted ekm wekm algorithms it shows that ekm algorithms become a special case of the wekm algorithms when the weights of the latter are constant value it also shows that in general the weighted ekm algorithms have smaller absolute error and faster convergence speed than the ekm algorithms which make them very attractive for real time applications of fuzzy logic system four numerical examples are used to illustrate and analyze the performance of wekm algorithms

tuning clustering in random networks with arbitrary degree distributions we present a generator of random networks where both the degree dependent clustering coefficient and the degree distribution are tunable following the same philosophy as in the configuration model the degree distribution and the clustering coefficient for each class of nodes of degree k are fixed ad hoc and a priori the algorithm generates corresponding topologies by applying first a closure of triangles and second the classical closure of remaining free stubs the procedure unveils an universal relation among clustering and degree degree correlations for all networks where the level of assortativity establishes an upper limit to the level of clustering maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior correlation measures in real networks are seen to observe this structural bound

fuzzy weighted average a max min paired elimination method by the use of max min paired elimination an efficient method for obtaining the fuzzy weighted average fwa was developed this approach is much more efficient than either the approach developed by dong and wong 1 or the improved approach developed by liou and wang 2 the computational requirements for the method of dong and wong are 22n and the largest computational requirements for the improved method of liou and wang are 2 n n 1 the computational requirements for the proposed approach are proportional to the problem size n and the total computational requirements are 2 n 1 the same example used by dong and wong is used to illustrate the approach in addition a more complicated problem is also solved

a column generation algorithm for choice based network revenue management during the past few years there has been a trend to enrich traditional revenue management models built upon the independent demand paradigm by accounting for customer choice behavior this extension involves both modeling and computational challenges one way to describe choice behavior is to assume that each customer belongs to a segment which is characterized by a consideration set i e a subset of the products provided by the firm that a customer views as options customers choose a particular product according to a multinomial logit criterion a model widely used in the marketing literature in this paper we consider the choice based deterministic linear programming model cdlp of gallego et al 2004 gallego g g iyengar r phillips a dubey 2004 managing flexible products on a network technical report corc tr 2004 01 department of industrial engineering and operations research columbia university new york and the follow up dynamic programming decomposition heuristic of van ryzin and liu 2008 van ryzin g j q liu 2008 on the choice based linear programming model for network revenue management manufacturing service oper management10 2 288 310 we focus on the more general version of these models where customers belong to overlapping segments to solve the cdlp for real size networks we need to develop a column generation algorithm we prove that the associated column generation subproblem is indeed np hard and propose a simple greedy heuristic to overcome the complexity of an exact algorithm our computational results show that the heuristic is quite effective and that the overall approach leads to high quality practical solutions

class of correlated random networks with hidden variables we study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices we find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices the expressions obtained are checked by means of numerical simulations in a particular example the general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure we also present an extension of the class to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

the multidimensional 0 1 knapsack problem an overview abstract the multidimensional 0 1 knapsack problem is one of the most well known integer programming problems and has received wide attention from the operational research community during the last four decades although recent advances have made possible the solution of medium size instances solving this np hard problem remains a very interesting challenge especially when the number of constraints increases this paper surveys the main results published in the literature the focus is on the theoretical properties as well as approximate or exact solutions of this special 0 1 program

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks

higher order assortativity in complex networks abstract assortativity was first introduced by newman and has been extensively studied and applied to many real world networked systems since then assortativity is a graph metric and describes the tendency of high degree nodes to be directly connected to high degree nodes and low degree nodes to low degree nodes it can be interpreted as a first order measure of the connection between nodes i e the first autocorrelation of the degree degree vector even though assortativity has been used so extensively to the author s knowledge no attempt has been made to extend it theoretically indeed newman assortativity is about being adjacent but even though two nodes may not by connected through an edge they could have possibly a strong level of connectivity through a large number of walks and paths between them this is the scope of our paper we introduce for undirected and unweighted networks higher order assortativity by extending the newman index based on a suitable choice of the matrix driving the connections higher order assortativity be defined for paths shortest paths and random walks of a given length the newman assortativity is a particular case of each of these measures when the matrix is the adjacency matrix or in other words the autocorrelation is of order 1 our higher order assortativity indices help discriminating networks having the same newman index and may reveal new topological network features an application to airline network italy and us and to enron email network as well as examples and simulations are discussed

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved