the analysis and dissimilarity comparison of community structure abstract based on a database of collaboration recording in econophysics scientists and other networks hierarchical clustering method and the algorithm of girvan and newman are applied to detect their community structure the interesting results for community structure of econophysicists collaboration network are shown a dissimilarity function d is proposed to quantitatively measure the difference between community structures obtained by different methods using this measurement the differences between the process and community results obtained by aforementioned algorithms are given the effectiveness of hierarchical clustering method and gn algorithm for detecting community structure in various networks is discussed

on the exact solution of a facility layout problem we consider the layout problem of arranging a number of departments on a line this problem is known as single row facility layout the problem is very difficult to be solved in fact it has as a particular case the linear ordering problem which is strongly np hard in this paper a new mixed integer linear programming model is proposed for the problem theoretical arguments as well as computational results are given which demonstrate the efficiency of the new model relatively to previous mixed integer linear programming models proposed for the problem

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

semidefinite relaxations of ordering problems ordering problems assign weights to each ordering and ask to find an ordering of maximum weight we consider problems where the cost function is either linear or quadratic in the first case there is a given profit if the element u is before v in the ordering in the second case the profit depends on whether u is before v and r is before s the linear ordering problem is well studied with exact solution methods based on polyhedral relaxations the quadratic ordering problem does not seem to have attracted similar attention we present a systematic investigation of semidefinite optimization based relaxations for the quadratic ordering problem extending and improving existing approaches we show the efficiency of our relaxations by providing computational experience on a variety of problem classes

an efficient tabu algorithm for the single row facility layout problem the general goal of the facility layout problem is to arrange a given number of facilities to minimize the total cost associated with the known or projected interactions between them one of the special classes of the facility layout problem is the single row facility layout problem srflp which consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line this paper first presents and proves a theorem to find the optimal solution of a special case of srflp the results obtained by this theorem prove to be very useful in reducing the computational efforts when a new algorithm based on tabu search for the srflp is proposed in this paper computational results of the proposed algorithm on benchmark problems show the greater efficiency of the algorithm compared to the other heuristics for solving the srflp

experimental analysis of simulated annealing based algorithms for the layout problem abstract in this paper results from an experimental analysis involving the 2 way and 3 way exchange algorithms a modified penalty algorithm the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented the hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing it is tested on single row layout problems with facilities of unequal area and multi row layout problems with facilities of equal area the algorithm produced solutions better than those previously reported in the literature for two of the larger single row problems and five multi row layout problems for all the other single row problems and eight of ten multi row layout test problems it produced the best known solutions the hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms but requires more computation time than simulated annealing

a polyhedral approach to the single row facility layout problem the single row facility layout problem srflp is the np hard problem of arranging facilities on a line while minimizing a weighted sum of the distances between facility pairs in this paper a detailed polyhedral study of the srflp is performed and several huge classes of valid and facet inducing inequalities are derived some separation heuristics are presented along with a primal heuristic based on multi dimensional scaling finally a branch and cut algorithm is described and some encouraging computational results are given

nonlocal evolution of weighted scale free networks we introduce the notion of globally updating evolution for a class of weighted networks in which the weight of a link is characterized by the amount of data packet transport flowing through it by noting that the packet transport over the network is determined nonlocally this approach can explain the generic nonlinear scaling between the strength and the degree of a node we demonstrate by a simple model that the strength driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule generating the power law behaviors in degree and in strength simultaneously

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

the effect of weight on community structure of networks abstract the effect of weight on community structures is investigated in this paper we use weighted modularity q w to evaluate the partitions and weighted extremal optimization algorithm to detect communities starting from empirical and idealized weighted networks the matching between weights and edges are disturbed then using similarity function s to measure the difference between community structures it is found that the redistribution of weights does strongly affect the community structure especially in dense networks this indicates that the community structure in networks is a suitable property to reflect the role of weight

a class of improved algorithms for detecting communities in complex networks abstract detecting communities in complex networks is of considerable importance for understanding both the structure and function of the networks here we propose a class of improved algorithms for community detection by combining the betweenness algorithm of girvan and newman with the edge weight defined by the edge clustering coefficient the improved algorithms are tested on some artificial and real world networks and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases in addition the technique for improving the betweenness algorithm in this paper thanks to its compatibility can directly be applied to various detection algorithms

on the one dimensional space allocation problem the one dimensional space allocation problem odsap arises when locating rooms along a corridor when setting books on a shelf when allocating information items among the cylinders of a magnetic disk or when storing products in certain warehouses the rooms objects to be located have a known length or width and for each pair of rooms there is a given number of trips between them the problem is to find a sequencing of the rooms which minimizes the total traveled distance this paper deals first with two particular cases in the rooted tree case previous results obtained by adolphson and t c hu for the linear ordering problem are extended and provide efficient solution methods in addition it is shown that most of the assumptions made by adolphson and hu are necessary since relaxing any of them leads to an np complete problem in the case of independent destinations solved by bergmans and pratt when all lengths are equal a unimodality property is shown for an optimum solution but this is not sufficient to lead to a good algorithm and the problem is shown to be np complete for the general problem an exact algorithm using dynamic programming is described and computationally tested

single row facility layout problem using a permutation based genetic algorithm in this paper a permutation based genetic algorithm ga is applied to the np hard problem of arranging a number of facilities on a line with minimum cost known as the single row facility layout problem srflp the ga individuals are obtained by using some rule based as well as random permutations of the facilities which are then improved towards the optimum by means of specially designed crossover and mutation operators such schemes led the ga to handle the srflp as an unconstrained optimization problem in the computational experiments carried out with large size instances of sizes from 60 to 80 available in the literature the proposed ga improved several previously known best solutions

hybridizing variable neighborhood search with ant colony optimization for solving the single row facility layout problem abstract in this paper a hybrid algorithm based on variable neighborhood search and ant colony optimization is proposed to solve the single row facility layout problem in the proposed algorithm three neighborhood structures are utilized to enhance the exploitation ability meanwhile new gain techniques are developed to reduce the mathematical calculations of the objective function values furthermore ant colony optimization as the shaking step is used to avoid being stuck at the local optima in addition a novel pheromone updating rule has been proposed based on both the best and worst solutions of the ants a reverse criterion based on edit distance measure is applied to help ants to converge to the best solution and reduce the solution space finally numerical simulation is carried out based on the benchmark instances and the comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm

scale free properties of weighted networks with connectivity driven topology abstract the rate equations are used to study the scale free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices an analysis of these equations shows that the degree distribution and thereby the weight distribution remain unchanged when the probability rate of attaching new nodes is replaced with an unnormalized rate determined by the ratio of the degree of a randomly selected old node to the maximal node degree at the current stage of the network evolution such a modification of the attachment rule is argued to accelerate considerable numerical simulations of both unweighted and weighted networks belonging to the class of investigated evolving systems it is also proved that the studied rate equations have a solution corresponding to the total weight concentrated at individual vertices distribution displaying the power law behavior for asymptotically large weights

accuracy and precision of methods for community identification in weighted networks based on brief review of approaches for community identification and measurement for sensitivity characterization the accuracy and precision of several approaches for detecting communities in weighted networks are investigated in weighted networks the community structure should take both links and link weights into account and the partition of networks should be evaluated by weighted modularity q w the results reveal that link weight has important effects on communities especially in dense networks potts model and weighted extremal optimization weo algorithm work well on weighted networks then potts model and weo algorithms are used to detect communities in rhesus monkey network the results gives nice understanding for real community structure

statistics of weighted treelike networks we study the statistics of growing networks with a tree topology in which each link carries a weight k i k j theta where k i and k j are the node degrees at the end points of link ij network growth is governed by preferential attachment in which a newly added node attaches to a node of degree k with rate a k k lambda for general values of theta and lambda we compute the total weight of a network as a function of the number of nodes n and the distribution of link weights generically the total weight grows as n for lambda theta 1 and superlinearly otherwise the link weight distribution is predicted to have a power law form that is modified by a logarithmic correction for the case lambda 0 we also determine the node strength defined as the sum of the weights of the links that attach to the node as function of k using known results for degree correlations we deduce the scaling of the node strength on k and n

modeling the evolution of weighted networks we present a general model for the growth of weighted networks in which the structural growth is coupled with the edges weight dynamical evolution the model is based on a simple weight driven dynamics and a weights reinforcement mechanism coupled to the local network growth that coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real world networks the model generates weighted graphs exhibiting the statistical properties observed in several real world systems in particular the model yields a nontrivial time evolution of vertices properties and scale free behavior with exponents depending on the microscopic parameters characterizing the coupling rules very interestingly the generated graphs spontaneously achieve a complex hierarchical architecture characterized by clustering and connectivity correlations varying as a function of the vertices degree

weighted networks of scientific communication the measurement and topological role of weight abstract in order to take the weight of connection into consideration and to find a natural measurement of weight we have collected papers in econophysics and constructed a network of scientific communication to integrate idea transportation among econophysicists by collaboration citation and personal discussion some basic statistics such as weight per degree are discussed in fan et al j mod phys b 17 19 2004 2505 in this paper by including the papers published recently further statistical results for the network are reported clustering coefficient of weighted networks is introduced and empirically studied in this network we also compare the typical statistics on this network under different weight assignments including random and inverse weight the conclusion from weight redistributed network is helpful to the investigation of the topological role of weight

load distribution in weighted complex networks we study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex the optimal path along which the total cost is minimum crucially depends on the cost distribution function p c c in the strong disorder limit where p c c ensuremath sim c ensuremath 1 the load distribution follows a power law both in the erd ifmmode mbox h o else h o fi s r enyi er random graphs and in the scale free sf networks and its characteristics are determined by the structure of the minimum spanning tree the distribution of loads at vertices with a given vertex degree also follows the sf nature similar to the whole load distribution implying that the global transport property is not correlated to the local structural information finally we measure the effect of disorder by the correlation coefficient between vertex degree and load finding that it is larger for er networks than for sf networks

tabu search for the single row facility layout problem using exhaustive 2 opt and insertion neighborhoods abstract the single row facility layout problem srflp is the problem of arranging facilities with given lengths on a line while minimizing the weighted sum of the distances between all pairs of facilities the problem is np hard in this paper we present two tabu search implementations one involving an exhaustive search of the 2 opt neighborhood and the other involving an exhaustive search of the insertion neighborhood we also present techniques to significantly speed up the search of the two neighborhoods our computational experiments show that the speed up techniques are effective and our tabu search implementations are competitive our tabu search implementations improved previously known best solutions for 23 out of the 43 large sized srflp benchmark instances

weight driven growing networks we study growing networks in which each link carries a certain weight randomly assigned at birth and fixed thereafter the weight of a node is defined as the sum of the weights of the links attached to the node and the network grows via the simplest weight driven rule a newly added node is connected to an already existing node with the probability which is proportional to the weight of that node we show that the node weight distribution n w has a universal tail that is it is independent of the link weight distribution n w approximately w 3 as w infinity results are particularly neat for the exponential link weight distribution when n w is algebraic over the entire weight range

efficient models for the facility layout problem abstract in this paper two new models of the facility layout problem are presented linear continuous with absolute values in the objective function and constraints and linear mixed integer the linear mixed integer models have lesser number of integer variables than any other existing formulation for the facility layout problem while most other linear mixed integer models available in the literature have been obtained through a linearization of the quadratic assignment problem the ones presented in this paper are not the continuous models have an even more compact form an advantage of the formulations presented in this paper is that the location of sites need not be known a priori more importantly two of the formulations model the layout problem with facilities of unequal area solving the models presented with an unconstrained optimization algorithm yields good quality suboptimal solutions in a relatively low computation time the continuous models appear to be more useful for solving the facility layout problem than other models published in the literature

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

an exact approach to the one dimensional facility layout problem the one dimensional facility layout problem is concerned with arranging n departments of given lengths on a line while minimizing the weighted sum of the distances between all pairs of departments the problem is np hard because it is a generalization of the minimum linear arrangement problem in this paper a 0 1 quadratic programming model consisting of only o n2 0 1 variables is proposed for the problem subsequently this model is cast as an equivalent mixed integer program and then reduced by preprocessing next additional redundant constraints are introduced and linearized in a higher space to achieve an equivalent mixed 0 1 linear program whose continuous relaxation provides an approximation of the convex hull of solutions to the quadratic program it is shown that the resulting mixed 0 1 linear program is more efficient than previously published mixed integer formulations in the computational results several problem instances taken from the literature were efficiently solved to optimality moreover it is now possible to efficiently solve problems of a larger size

near optimal depth constrained codes this note considers an n letter alphabet in which the ith letter is accessed with probability p sub i the problem is to design efficient algorithms for constructing near optimal depth constrained huffman and alphabetic codes we recast the problem as one of determining a probability vector q sup q sup sub 1 q sup sub n in an appropriate convex set s so as to minimize the relative entropy d p spl par q over all q spl isin s methods from convex optimization give an explicit solution for q sup in terms of p we show that the huffman and alphabetic codes so constructed are within 1 and 2 bits of the corresponding optimal depth constrained codes