link prediction based on local information considering preferential attachment abstract link prediction in complex networks has attracted much attention in many fields in this paper a common neighbors plus preferential attachment index is presented to estimate the likelihood of the existence of a link between two nodes based on local information of the nearest neighbors numerical experiments on six real networks demonstrated the high effectiveness and efficiency of the new index compared with five well known and widely accepted indices the common neighbors resource allocation index preferential attachment index local path index and katz index the new index provides competitively accurate prediction with local path index and katz index while has less computational complexity and is more accurate than the other two indices

sets of efficient points in a normed space abstract sets of efficient points in a normed space with respect to the distances to the points of a given compact set are geometrically characterized hull and closure properties are obtained these results are relevant to geometry of normed spaces and are mostly useful in the context of location theory

solving general continuous single facility location problems by cutting planes abstract a unified cutting plane method is proposed to solve a large class of continuous single facility location problems these include both minisum and minimax problems with mixed norms and convex transportation costs the method provides an easy stopping rule and permits the post optimal determination of an outer approximation to near optimality regions two examples are given which show the power of the method extensive computational results in dimension two and higher are reported

on the uniqueness of optimal solutions in continuous location theory abstract this paper deals with the uniqueness of an optimal solution in general continuous single facility minisum and minimax location problems we define the concept of an s norm and obtain general conditions which guarantee the existence of a unique optimal location some consequences for the uniqueness of optimal locations in multi facility location problems are discussed

huneke wiegand conjecture for complete intersection numerical semigroup rings abstract we give a positive answer to the huneke wiegand conjecture for monomial ideals over free numerical semigroup rings and for two generated monomial ideals over complete intersection numerical semigroup rings

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

on efficient solutions to multiple objective mathematical programs this note develops properties of quasi efficient solutions and explores interrelationships to the classical concept of efficiency in particular a point is a quasi efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives this result is then used to characterize the set of quasi efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives

a geometrical solution for quadratic bicriteria location models this paper deals with a single facility unweighted quadratic bicriteria location problem defined in the continuous space first we describe an analytical method for constructing the set of pareto optimal locations for this problem based on the farthest point voronoi diagram then we present an analytical method for finding the solution to the scalarized location problems based on the pareto optimal locations the analytical results enable planners to carry out some sensitivity analyses since both methods are based entirely on geometrical analysis they can be understood intuitively

when facilities coincide exact optimality conditions in multifacility location abstract in continuous minisum multifacility location problems it has been observed that optimal solutions often involve coincidences of facilities this paper gives a complete analysis by way of subdifferential calculus of the exact optimality conditions at such solutions these conditions are expressed as the existence of a multidimensional conservative flow in a network satisfying a nonlinear constraint on each edge by way of network flow theory a description with a minimal number of variables is obtained this procedure is illustrated by several examples showing how it enables a sensitivity analysis of the optimal solution with respect to the weights of the problem the optimality conditions are shown to be always directly verifiable if the network is a tree necessary conditions for coincidences at an optimal solution which previously appeared in the literature are generalized and it is shown in which cases these are also sufficient

on minimax optimization problems we give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk 1 functions such that a solution to the minimax problem with thosek 1 functions is a solution to the minimax problem with all functions we show that convexity is necessary and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function

directional bias of the lp norm this paper concerns the use of the lp norm for estimating travel distances in a transportation network in previous empirical studies values of the parameter p 2 have been employed to characterize road networks after a detailed study of the directional bias of the lp norm it is shown here that such values need never be considered since the same degree of accuracy is obtained with a value of p in the interval 1 2 after rotating the axes 45

some properties of location problems with block and round norms the point objective problem and the weber problem are two well known formulations for locating a new facility with respect to a set of fixed facilities when locations are represented as points on a plane the point objective problem is a multiple objective formulation of minimizing the distance from a variable point to each of the fixed points similarly the weber problem is a single objective formulation of minimizing the sum of transportation costs between the variable point and the fixed points where transportation cost is a function of distance generalizing solution properties for these problems from distance measures given by the euclidean rectilinear ip and one infinity norms this paper develops solution properties under the broad classes of distance measures given by block and round norms for the point objective problem we show that i the efficient set for all round norms is the convex hull of the set of fixed points and ii the efficient set under a block norm tends to the convex hull for a sequence of block norms approaching a round norm for the weber problem we prove that i an optimal location for any block norm may be found in a finite set of intersection points belonging to the convex hull and ii this set tends to the convex hull for a sequence of block norms approaching a round norm finally we use these results to propose a synthesis of some of the main properties in continuous and network location theory

decoupling process for better synchronizability on scale free networks we propose a decoupling process performed in scale free networks to enhance the synchronizability of the network together with preserving the scale free structure simulation results show that the decoupling process can effectively promote the network synchronizability which is measured in terms of eigenratio of the coupling matrix moreover we investigate the correlation between some important structural properties and the collective synchronization and find that the maximum vertex betweenness seems to be the most strongly correlated with the synchronizability among the major structural features considered we explain the effect of the decoupling process from a viewpoint of coupling information transmission our work provides some evidence that the dynamics of synchronization is related to that of information or vehicle traffic because of the low cost in modifying the coupling network the decoupling process may have potential applications

simpson points in planar problems with locational constraints the polyhedral gauge case in this paper we address the problem of finding simpson points in planar models with locational constraints when distances are measured by polyhedral gauges making use of the results we have stated in a previous paper we show here the existence of a finite set of points in the plane independent of the weights associated with the users that contains at least a simpson point connection between simpson points as a result of a voting process and weber points as the outcome of a planning process are explored it is shown by means of an example that the existing relations for the unconstrained case are no longer true when locational constraints are imposed in order to reconcile both voting and planning processes a biobjective problem is described for which we construct a finite dominating set

localization in single facility location abstract a well known localization theorem in continuous single facility location of wendell and hurter states that any weber problem in the plane in which all norms are identical admits an optimal solution within the convex hull of the destination points in this paper it is shown that this result fails for general norms as soon as the dimension is at least three a new localization theorem is then proposed that is valid under very general conditions this makes it possible to consider most unconstrained single facility location problems as constrained problems it is indicated how to construct an easily implemented form of such constraints

attack vulnerability of complex networks we study the response of complex networks subject to attacks on vertices and edges several existing complex network models as well as real world networks of scientific collaborations and internet traffic are numerically investigated and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph for each case of attacks on vertices and edges four different attacking strategies are used removals by the descending order of the degree and the betweenness centrality calculated for either the initial network or the current network during the removal procedure it is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network suggesting that the network structure changes as important vertices or edges are removed furthermore the correlation between the betweenness centrality and the degree in complex networks is studied

huneke wiegand conjecture and change of rings abstract let r be a cohen macaulay local ring of dimension one with a canonical module k r let i be a faithful ideal of r we explore the problem of when i r i is torsionfree where i hom r i k r we prove that if r has multiplicity at most 6 then i is isomorphic to r or k r as an r module once i r i is torsionfree this result is applied to monomial ideals of numerical semigroup rings a higher dimensional assertion is also discussed

the effect of axis rotation on distance estimation abstract the objective of this paper is to evaluate the usefulness of the weighted l p norm as a distance measure when axis rotation is included to obtain the best fit we compare the weighted l p and euclidean norms in an empirical study of 18 major country and city road networks a substantial improvement in accuracy is obtained with the weighted l p norm for networks with a significant component of rectangular travel we show that the weighted l p norm and by inference other multi parameter distance estimators are justified in practice provided the reference axes are oriented properly to model the directional bias inherent in the network

estimating road distances by mathematical functions abstract in recent publications various distance functions have been proposed for estimating road distances and the parameters of these functions have been determined for the u s a as a whole as well as for several subregions in consideration of the degree of accuracy attainable for the regions surveyed and the amount of work entailed by parameter determination it has been suggested that a two parameter function should be used in the first instance whenever distance estimating functions are required for other geographical regions this method was applied to a european region the federal republic of germany in contrast to the results obtained for the u s a there were only slight increases in the degree of accuracy of the estimates when single parameter distance functions were replaced by multiparametric ones since moreover the determination of a second or even a third parameter entails a great deal of work it is doubtful whether the use of a two parameter function can continue to be regarded as an economically justifiable method in europe

using block norms for location modeling in formulating a continuous location model with facilities represented as points in rn e g typically in the plane one must characterize the distance between two points as a function of their coordinates two criteria in selecting a distance function are 1 to obtain good approximations of actual distances and 2 to obtain a mathematical model of the location problem that is easy to solve in this paper we show how a class of norms with polygonal contours called block norms can yield attractive choices as distance functions with respect to these criteria in particular we consider the following relevant properties of block norms they generalize the concepts of rectilinear or city block travel they are dense in the set of all norms they have interesting travel interpretations in the plane they can be expressed as a sum of the absolute values of linear functions they often give better approximations to actual highway distances than the most frequently used family of norms the lp norms and finally they yield linear programming formulations of certain facility location problems i e the weber problem and the rawls problem

auslander reiten conjecture and auslander reiten duality abstract motivated by a result of araya we extend the auslander reiten duality theorem to cohen macaulay local rings we also study the auslander reiten conjecture which is rooted in nakayama s work on finite dimensional algebras one of our results detects a certain condition that forces the conjecture to hold over local rings of positive depth

gbsss the generalized big square small square method for planar single facility location abstract big square small square is a geometrical branch and bound algorithm devised by p hansen et al or 33 1251 1265 for the solution of constrained planar minisum single facility location problems with l p norms and continuous non decreasing costfunctions the method basically works by splitting the studied planar region into squares and either rejecting or further processing these squares by the evaluation of a lower bound we present a modified version of this algorithm aimed at correcting a small failure to converge accelerating the calculations minimising the information to be stored and most importantly determining a region of near optimality furthermore the method is applicable to any planar single facility problem with distances measured by mixed norms and as an objective any continuous function of the distances this includes nearly all the models which have been proposed in the literature

convergence of the weiszfeld algorithm for weber problems using a generalized distance function this paper considers a generalization of the single and multisource weber problem for the case when the distance function is some power k of the usual ip distance properties of the generalized problem are established and an appropriate generalization of the weiszfeld iterative approach is given a convergence proof is supplied for an approximation to the original problem under certain restrictions on p and k

parametric distance functions vs nonparametric neural networks for estimating road travel distances abstract measuring and storing actual road travel distances between the points of a region is often not feasible and it is a common practice to estimate them the usual approach is to use distance estimators which are parameterized functions of the coordinates of the points we propose to use nonparametric approaches using neural networks for estimating actual distances we consider multi layer perceptrons trained with the back propagation rule and regression neural networks implementing nonparametric regression using gaussian kernels we also consider training multiple estimators and combining them using voting and stacking on a real world study using cities drawn from turkey we found out that these nonparametric approaches are more accurate than the parametric distance functions estimating actual distances has many applications in location and distribution theory

use of reference points for solving monlp problems abstract the paper discusses a scalar problem that uses a reference point for solving the multiobjective nonlinear programming monlp problem some properties of the solution of this scalar problem are described in order to improve the achieved value of one criterion only the corresponding component of the reference point has to be changed

the suitability of the weighted lp norm in estimating actual road distances abstract the weighted l p norm suggested as a way to estimate actual road distances takes time and effort to calculate because it requires two parameters compared to the weighted euclidean norm a function requiring only one parameter which is relatively easy to obtain the weighted l p norm yields considerably better estimates for some countries and only negligible improvements for others this paper evaluates whether on the basis of easy to obtain data characterizing the road network of a particular area one can predict the extent of the improvement in estimate accuracy such an ability to predetermine estimate accuracy would help researchers decide when to use the expensive l p norm the investigation shows however that no such relationship can be proven the extent of the improvement in estimate accuracy offered by the weighted l p norm cannot be predicted

a primal dual algorithm for the fermat weber problem involving mixed gauges we give a new algorithm for solving the fermat weber location problem involving mixed gauges this algorithm which is derived from the partial inverse method developed by j e spingarn simultaneously generates two sequences globally converging to a primal and a dual solution respectively in addition the updating formulae are very simple a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions when polyhedral gauges are used we show that the algorithm terminates in a finite number of steps provided that the set of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property is violated finally numerical results are reported and we discuss possible extensions of these results

error bounds for the approximative solution of restricted planar location problems abstract facility location problems in the plane play an important role in mathematical programming when looking for new locations in modeling real world problems we are often confronted with forbidden regions that are not feasible for the placement of new locations furthermore these forbidden regions may have complicated shapes even if we require them to be convex it may be more useful or even necessary to use approximations of such forbidden regions when trying to solve location problems in this paper we develop error bounds for the approximative solution of restricted planar location problems using the so called sandwich algorithm the number of approximation steps required to achieve a specified error bound is analyzed as examples of these approximation schemes we discuss round norms and polyhedral norms computational tests are also included

the minisum and minimax location problems revisited the minisum minimax problem consists of locating a single facility in the plane with the aim of minimizing the sum of the weighted distances the maximum weighted distance to m given points we present two solution methods for generalized versions of these problems in which i location is restricted to the union of a finite number of convex polygons ii distances are approximated by norms that may differ with the given points and iii transportation costs are increasing and continuous functions of distance computational experience is described

location and shape of a rectangular facility in r n convexity properties in this paper we address a generalization of the weber problem in which we seek for the center and the shape of a rectangle the facility minimizing the average distance to a given set the demand set which is not assumed to be finite some theoretical properties of the average distance are studied and an expression for its gradient involving solely expected distances to rectangles is obtained this enables the resolution of the problem by standard optimization techniques

continuous multifacility ordered median location problems abstract in this paper we propose a general methodology for solving a broad class of continuous multifacility location problems in any dimension and with l norms proposing two different methodologies 1 by a new second order cone mixed integer programming formulation and 2 by formulating a sequence of semidefinite programs that converges to the solution of the problem each of these relaxed problems solvable with sdp solvers in polynomial time

on pareto optima the fermat weber problem and polyhedral gauges this paper deals with multiobjective programming in which the objective functions are nonsymmetric distances derived from different gauges to the points of a fixed finite subset of n it emphasizes the case in which the gauges are polyhedral in this framework the following result is known if the gauges are polyhedral then each pareto optimum is the solution to a fermat weber problem with strictly positive coefficients we give a new proof of this result and we show that it is useful in finding the whole set of efficient points of a location problem with polyhedral gauges also we characterize polyhedral gauges in terms of a property of their subdifferential

hull properties in location problems abstract some properties of the solution set for single and multifacility continuous location problems with l p distances are given a set reduction algorithm is developed for problems in k dimensional space having rectangular distances

geometrical properties of the fermat weber problem abstract this paper is devoted to the fermat weber problem with mixed gauges in order to take into account nonsymmetric distances a geometrical description of the set of solutions is obtained then the concept of metric hull is defined general sufficient conditions are given such that the metric hull of existing facilities intersects the set of optimal locations particularly it is shown that an optimal location can be found in the metric hull in dimension two whatever the gauges are and in dimension n with the rectilinear norm the connection between metric hull convex hull and octagonal hull is studied

optimal expected distance separating halfspace one recently proposed criterion to separate two data sets in discriminant analysis is to use a hyperplane which minimizes the sum of distances to it from all the misclassified data points here all distances are supposed to be measured by way of some fixed norm while misclassification means lying in the wrong halfspace in this paper we study the problem of determining such an optimal halfspace when points are distributed according to an arbitrary random vector x in rd in the unconstrained case in dimension d we prove that any optimal separating halfspace always balances the misclassified points moreover under polyhedrality assumptions on the support of x there always exists an optimal separating halfspace passing through d affinely independent points these results extend in a natural way when different norms or a fixed gauge are used to measure distances and we allow constraints modeling that certain points are forced to be correctly classified

an approach to location models involving sets as existing facilities in this paper we deal with single facility location problems in a general normed space in which the existing facilities are represented by convex sets of points the criterion to be satisfied by the service facility is the minimization of an increasing convex function of the distances from the service facility to the closest point of each demand set we obtain a geometrical characterization of the set of optimal solutions for this problem two remarkable cases the classical weber problem and the minimax problem with demand sets are studied as particular instances of our problem finally for the planar polyhedral case we give an algorithm to find the solution set of the considered problems

an algorithm for the minimax weber problem abstract the paper presents an algorithm for finding the weighted absolute center of a given set of points in the euclidean plane the algorithm is a specialized implementation of the method of feasible directions the presentation includes a proof of convergence as well as computational experience

optimal locations and inner products abstract in a normed space x we consider objective functions which depend on the distances between a variable point and the points of certain finite sets a a point where such a function attains its minimum on x is generically called an optimal location in this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull of a or barycenters of points of a with well chosen weights we thus generalize several classical results about characterization of inner product spaces

a generalized weber problem with different gauges for different regions abstract this paper considers a generalized variation of the weber problem gvwp on the plane in which a straight line divides the plane into two regions and different gauges are employed to measure the distances in different regions gvwp is a generalized problem of some well studied variations of weber problem vwp in the following aspects 1 both the unconstrained and constrained problems are taken into consideration 2 the more general distance measuring functions gauges are employed to measure distances instead of the usually used l p norms therefore the gvwp is more practical and applicable in practice gvwp is nonconvex as vwp and as a generalized problem it is more complex than the latter in this paper the gvwp is divided into three subproblems which are optimally solved two subproblems are reformulated into monotone linear variational inequalities lvis and then solved by a projection contraction method while the third subproblem is divided into some convex problems and the golden section search is used to solve them by dividing the gvwp into three subproblems and solving these subproblems optimally an algorithm which can obtain the global optimal solution of gvwp is proposed preliminary numerical results are reported to verify the evident effectiveness of the proposed algorithm

a discretizing algorithm for location problems abstract a new and simple methodology is proposed to solve both constrained and unconstrained planar continuous single facility location problems as particular instances the classical location problems with mixed gauges can be solved theoretical convergence is proved and numerical examples are given showing a fast convergence in a small number of steps