We consider network design games with weighted players and uniform edge capacities and study their Nash equilibria. In these games, each player has to choose a path from her source to her sink through a network subject to the constraint that the total weight of all players using an edge within their chosen path does not exceed the capacity of the edge. The fixed cost of each edge that is used by some player is shared among the players using the edge by charging each player a fraction of the edge's cost equal to the ratio of her weight to the total weight of all players using the edge. We show that there exist instances of capacitated network design games with weighted players and uniform capacities that do not admit a Nash equilibrium even in the case that all players share the same source and sink. Moreover, we show that it is strongly -hard to decide whether a given instance admits a Nash equilibrium even if a feasible solution for the underlying network design problem is guaranteed to exist. In contrast, we prove that, for series-parallel graphs, there always exists a Nash equilibrium whose total cost equals the cost of an optimal solution of the corresponding network design problem and provide an (exponential-time) algorithm to compute this equilibrium. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly -hard. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>This article considers the problem of designing a two-level network where the upper level consists of a backbone ring network connecting the so-called hub nodes, and the lower level is formed by access ring networks that connect the non-hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to , thus resulting in a ring/ -rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch-and-cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable time. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>The automated real time control of an electrical network is achieved through the estimation of its state using phasor measurement units. Given an undirected graph representing the network, we study the problem of finding the minimum number of phasor measurement units to place on the edges such that the graph is fully observed. This problem is also known as the Power Edge Set problem, a variant of the Power Dominating Set problem. It is naturally modeled using an iteration-indexed binary linear program, whose size turns out to be too large for practical purposes. We use a fixed-point argument to remove the iteration indices and obtain a more compact bilevel formulation. We then reformulate the latter to a single-level mixed-integer linear program, which performs better than the natural formulation. Lastly, we provide an algorithm that solves the bilevel program directly and much faster than a commercial solver can solve the previous models. We also discuss robust variants and extensions of the problem. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

]]>We study a location-routing problem in the context of capacitated vehicle routing. The input to the *k*-location capacitated vehicle routing problem (*k*-LocVRP) consists of a set of demand locations in a metric space and a fleet of *k* identical vehicles, each of capacity *Q*. The objective is to locate *k* depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for *k*-LocVRP. In obtaining this result, we introduce a common generalization of the *k-median* and *minimum spanning tree* problems (called *k* median forest), which might be of independent interest. We give a local-search based
-approximation algorithm for *k* median forest, which leads to a
-approximation algorithm for *k*-LocVRP, for any constant
. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

We consider a content distribution network (CDN) in which data hubs or servers are established in multiple locations to cater to local demands. The distributions of data to these hubs along with related network design problems (such as hub location and user assignment) are the key decision problems to consider to minimize the total routing cost. A new model for allocation of segments is introduced in Sen, Krishnamoorthy, Rangaraj and Narayanan, Comput Oper 62 (2015), 282–295, in which local preferences guide the database partitioning process, and the servers are fully connected to each other. In this article, we develop a simulated annealing (SA) approach (referred to as SA-mesh) to solve this problem and compare its performance with the corresponding mixed-integer linear programming (MILP) formulation. We also formulate a much harder variant of the problem in which servers are interconnected by a tree. We develop a SA algorithm (referred to as SA-tree) for this variant, in which a local search is incorporated to find a suboptimal tree backbone. We use a customized data structure based on linked lists to represent a solution in our algorithms. This enables our algorithms to scale to much larger instances of the problem. We use optimal solutions and the benchmarks obtained by CPLEX to justify the performance of our algorithms. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(1), 4–22 2016

]]>Ejection chain methods, which include the classical Lin–Kernighan (LK) procedure and the Stem-and-Cycle (S&C) reference structure, have been the source of the currently leading algorithms for large scale symmetric traveling salesman problems (STSP). Although these methods proved highly effective in generating large neighborhoods for symmetric instances, their potential application to the asymmetric setting of the problem (ATSP) introduces new challenges that require special consideration. This article extends our studies on the single-rooted S&C to examine the more advanced doubly-rooted (DR) reference structure. The DR structure, which is allied both to metaheuristics and network optimization, allows more complex network-related (alternating) paths to transition from one tour to another, and offers special advantages for the ATSP. Computational experiments on an extensive testbed exhibits superior performance for the DR neighborhood over its LK counterpart for the ATSP. We additionally show that a straightforward implementation of a DR ejection chain algorithm outperforms the best local search algorithms and obtains solutions comparable to those obtained by the currently most advanced special-purpose algorithms for the ATSP, while requiring dramatically reduced computation time. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(1), 23–33 2016

]]>This article studies the effect of partial coverage to extend the lifetime of wireless sensor networks and introduces a hybrid exact solution strategy that efficiently maximizes network lifetime. We consider a set of sensors used to provide coverage of discrete targets and transfer the information to the sink node via multi-hop wireless communication. An active sensor has one of the two roles: it is a source when it senses and transfers data; it is a relay if it only transfers data. Network lifetime is extended through the use of covers representing sensors role allocation and network topology. A hybrid column generation is used to identify the optimal operation schedules and roles allocation that maximize network lifetime. A constraint programming strategy is provided to identify profitable network configurations leading to extend network lifetime and to prove optimality of the solutions found. Moreover, an evolutionary algorithm is proposed to boost up the solution process and accelerate convergence. Extensive computational results demonstrate the effectiveness of the proposed approach. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(1), 34–53 2016

]]>We investigate a variant of the many-to-many hub location-routing problem which consists in partitioning the set of nodes of a graph into routes containing exactly one hub each, and determining an extra route interconnecting all hubs. A variable neighborhood descent with neighborhood structures based on remove/add, swap and exchange moves nested with routing and location operations is used as a local search procedure in a multistart algorithm. We also consider a sequential version of this local search in the multistart. In addition, a biased random-key genetic algorithm working with a local search routine, which also considers routing and location operations, is applied to the problem. To compare the heuristic solutions, we develop an integer programming formulation which is solved with a branch-and-cut algorithm. Capacity and path elimination constraints are added in a cutting plane fashion. The separation algorithms are based on the computation of min-cut trees and on the connected components of a support graph. Computational experiments were conducted on several benchmark instances of routing problems and show that the heuristics are effective on medium to large-sized instances, while the branch-and-cut algorithm solves small to medium sized problems to optimality. These algorithms were also compared with a commercial hybrid solver showing that the heuristics are quite competitive. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(1), 54–90 2016

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