The Stochastic Close-Enough Arc Routing Problem is a challenging problem where utility companies seek for a minimum-cost tour in order to collect meter consumption remotely. The stochasticity lies in the uncertainty of collecting data due to failed transmissions. In this article, we propose a mathematical formulation for this problem. We introduce some preprocessing properties, develop an exact method and several heuristics. Computational results from experiments are presented and analyzed. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017

]]>The minimum connected dominating set problem (MCDSP) has become increasingly important in recent years due to its applicability to mobile *ad hoc* networks and sensor grids. This paper presents a restricted swap-based neighborhood (RSN) tailored for solving MCDSP. This novel neighborhood structure is embedded into tabu Search (TS) and a perturbation mechanism is employed to enhance diversification. The proposed RSN-TS algorithm is tested on four sets of public benchmark instances widely used in the literature. The results demonstrate the efficacy of the proposed algorithm in terms of both solution quality and computational efficiency. In particular, the RSN-TS algorithm was able to improve the best known results on 41 out of the 97 problem instances while matching the best known results on all the remaining 56 instances. Furthermore, the article analyzes some key features of the proposed approach in order to identify its critical success factors. © 2017 Wiley Periodicals, Inc. NETWORKS, 2017

Given a directed graph with a capacity and a transit time for each arc and with single source and single sink nodes, the quickest flow problem is to find the minimum time horizon to send a given amount of flow from the source to the sink. This is one of the fundamental dynamic flow problems. Parametric search is one of the basic approaches to solving the problem. Recently, Lin and Jaillet (SODA, 2015) proposed an algorithm whose time complexity is the same as that of the minimum cost flow algorithm. Their algorithm employs a cost scaling technique, and its time complexity is weakly polynomial time. In this article, we modify their algorithm by adopting a technique to construct a strongly polynomial time algorithm for solving the minimum cost flow problem. The proposed algorithm runs in O time, where *n* and *m* are the numbers of nodes and arcs, respectively. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

In the *bidirected minimum Manhattan network problem*, given a set *T* of *n* terminals in the plane, no two terminals on the same horizontal or vertical line, we need to construct a network *N*(*T*) of minimum total length with the property that the edges of *N*(*T*) belong to the axis-parallel grid defined by *T* and are oriented in a such a way that every ordered pair of terminals is connected in *N*(*T*) by a directed Manhattan path. In this article, we present a polynomial factor 2-approximation algorithm for the bidirected minimum Manhattan network problem. © 2016 Wiley Periodicals, Inc. NETWORKS, 2016

This article focuses on the problem of minimizing the energy consumption in a resilient telecommunications network. For each demand, an edge-disjoint pair of paths (primary and backup) must be provided and the shared protection scheme is used. The energy consumption is due only to edges used in the no-fault scenario, but both primary and backup paths contribute to capacity consumption. We propose a projected formulation for the problem and show its effectiveness by comparing it with the complete formulation. We propose valid inequalities for both formulations. We evaluate the performances of the proposed formulations and valid inequalities through computational tests. Furthermore, we investigate the relationship between the shared and the dedicated protection version of the problem. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 6–22 2017

]]>Flows over time problems relate to finding optimal flows over a capacitated network where transit times on network arcs are explicitly considered. In this article, we study the problem of determining a minimum cost origin-destination path where the cost and the travel time of each arc depend on the time taken to travel from the origin to that particular arc along the path. We provide computational complexity results for this problem and an exact solution algorithm based on an enumeration scheme on the corresponding time expanded network. Finally, we show the efficiency of our approach through a number of experimental tests. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 23–32 2017

]]>In this article, we consider the Node-Weighted Dominating Steiner Problem. Given a graph with node weights and a set of terminal nodes, the goal is to find a connected node-induced subgraph of minimum weight, such that each terminal node is contained in or adjacent to some node in the chosen subgraph. The problem arises in applications in the design of telecommunication networks. Integer programming formulations for Steiner problems usually employ a variable for each edge. We introduce a formulation that only uses node variables and that models connectivity through node-cut inequalities, which can be separated in polynomial time. We discuss necessary and sufficient conditions for the model inequalities to define facets and we introduce a class of lifted partition-based inequalities, which can be used to strengthen the linear relaxation. Finally, we show that the polyhedron defined by these inequalities is integral if the underlying graph is a cycle where no two terminals are adjacent. In the general cycle setting, we show that we can get a complete description of the feasible solutions by lifting and projecting into a polytope with no more than twice the dimension. We also show that the well-known indegree equalities are implied by the lifted partition inequalities. Finally, we evaluate the effectiveness of the presented partition inequalities in computational experiments. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 33–51 2017

]]>This article is devoted to nonlinear single-path routing problems, which are known to be NP-hard even in the simplest cases. For solving these problems, we propose an algorithm inspired from Game Theory in which individual flows are allowed to independently select their path to minimize their own cost function. We design the cost function of the flows so that the resulting Nash equilibrium of the game provides an efficient approximation of the optimal solution. We establish the convergence of the algorithm and show that every optimal solution is a Nash equilibrium of the game. We also prove that if the objective function is a polynomial of degree , then the approximation ratio of the algorithm is . Experimental results show that the algorithm provides single-path routings with modest relative errors with respect to optimal solutions, while being several orders of magnitude faster than existing techniques. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 52–66 2017

]]>The budgeted minimum cost flow problem (BMCF(*K*)) with unit upgrading costs extends the classical minimum cost flow problem by allowing one to reduce the cost of at most *K* arcs. In this article, we consider complexity and algorithms for the special case of an uncapacitated network with just one source. By a reduction from 3-SAT we prove strong -completeness and inapproximability, even on directed acyclic graphs. On the positive side, we identify three polynomially solvable cases: on arborescences, on so-called tree-like graphs, and on instances with a constant number of sinks. Furthermore, we develop dynamic programs with pseudo-polynomial running time for the BMCF(*K*) problem on (directed) series-parallel graphs and (directed) graphs of bounded treewidth. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 67–82 2017

In the so-called network pricing problem an authority owns some arcs of the network and tolls them, while users travel between their origin and destination choosing their minimum cost path. In this article, we consider a unit toll scheme, and in particular the cases where the authority is imposing either the same toll on all of its arcs, or a toll proportional to a given parameter particular to each arc (for instance a per kilometer toll). We show that if tolls are all equal then the complexity of the problem is polynomial, whereas in case of proportional tolls it is pseudo-polynomial, proposing ad-hoc solution algorithms and relating these problems to the parametric shortest path problem. We then address a robust approach using an interval representation to take into consideration uncertainty on parameters. We show how to modify the algorithms for the deterministic case to solve the robust counterparts, maintaining their complexity class. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 83–93 2017

]]>In this work, a multiagent network flow problem is addressed, aiming at characterizing the properties of stable flows and allowing their computation. Two types of agents are considered: *transportation-agents*, that carry a flow of products on a given network and another agent, either a *producer* or a *customer*, who is willing to ship (receive, respectively), products. Every transportation-agent controls a set of arcs, each having a capacity that can be increased up to a certain point at a given cost. The other agent (i.e., the customer/producer) is interested in maximizing the flow transshipped through the network. To this aim, we assume it offers the transportation-agents a reward that is proportional to the realized flow value. This particular multiagent framework is referred to as a Multiagent network expansion game. We characterize and find particular stable strategies (i.e., Nash equilibria) that are of interest for this game. We particularly focus on the problem of finding a Nash Equilibrium and a sharing policy that maximize the value of the total flow. We prove that this problem is NP-hard in the strong sense and show how such a strategy can be characterized considering paths in specific auxiliary graphs. We also provide a mixed integer linear programming formulation to solve the problem. Computational experiments are provided to prove the effectiveness of our approach and derive some insights for practitioners. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 94–109 2017

During the planning of communication networks, the routing decision process (distributed and online) often remains decoupled from the network design process, that is, resource installation and allocation-planning process (centralized and offline). To reconcile both processes and take into account demand variability, we generalize the capacitated multicommodity fixed charge network design class of problems by including different types of fixed costs (installation and maintenance costs) and variable costs (routing costs) but also variable traffic demands over multiple periods. However, conventional integer programming methods can typically solve only small to medium size instances of this problem. Two major difficulties are encountered when using commercial solvers to solve the associated mixed integer programs: (i) problems are large scale and even solving the linear relaxation of the problem can be challenging; and (ii) the solver hardly find good feasible solutions for medium to large scale instances. As an alternative, we propose a Lagrangian approach for computing a lower bound by relaxing the flow conservation constraints such that the Lagrangian subproblem itself decomposes by node. Though this approach yields one subproblem per network node, solving the Lagrangian dual by means of the bundle method remains a complex computational tasks. However, it always provides a lower bound on the optimal solution. Moreover, based on this relaxation, we propose a Lagrangian heuristic that makes the approach more robust than a black-box usage of a Mixed Integer Programming (MIP) solver. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 110–123 2017

]]>Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph in such a way that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR-based Branch-and-Bound algorithm (DSATUR) is an effective exact algorithm for the VCP. One of its main drawback is that a lower bound is computed only once and it is never updated. We introduce a reduced graph which allows the computation of lower bounds at nodes of the branching tree. We compare the effectiveness of different classical VCP bounds, plus a new lower bound based on the -to- mapping between VCPs and Stable Set Problems. Our new DSATUR outperforms the state of the art for random VCP instances with high density, significantly increasing the size of instances solved to proven optimality. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 124–141 2017

]]>Given a graph
with
and
, we consider the metric cone
and the metric polytope
defined on
. These polyhedra are relaxations of several important problems in combinatorial optimization such as the max-cut problem and the multicommodity flow problem. They are known to have non-compact formulations via the cycle inequalities in the original space
and compact (i.e., polynomial size) extended formulations via the triangle inequalities defined on the complete graph
. In this article, we show that one can reduce the number of triangle inequalities to
and still have extended formulations for
and
. This is particularly interesting for sparse graphs when
, since formulations of size
variables and constraints are thus obtained. Moreover, the possibility of achieving further reduction in size for special classes of sparse graphs is investigated; it is shown that for the case of *series-parallel graphs*, for which the max-cut problem can be solved in linear time (Barahona, *Discr Appl Math* 13 (1986), 23–26), one can refine the above reduction to obtain extended formulations for
and
featuring
variables and constraints. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 142–150 2017

In dynamic flex-grid optical transport networks, Lightpath Admission Control (LAC) is the task of finding a Routing and Spectrum Assignment (RSA) solution for a current lightpath request; otherwise, the request is blocked if there are not enough free available resources. When rerouting is supported, one or more currently established lightpaths can be rerouted and/or assigned with a different spectrum in order to accommodate the current lightpath request. We propose LAC methods based on mixed integer linear programming that provide a RSA solution for the current request aiming to maximize the acceptance probability of future lightpath requests. When rerouting is supported, we consider that only one currently established lightpath can be rerouted. We compare the proposed methods with the traditional shortest path-based approach through simulation. Without lightpath rerouting, the blocking probability is significantly improved. With lightpath rerouting, the number of rerouting operations is significantly decreased while the blocking probability is marginally improved. Moreover, the blocking fairness between lightpaths with different spectrum widths is improved both with and without lightpath rerouting. In all cases, the CPU times of the mixed integer linear programming approaches are a few seconds, on average. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(1), 151–163 2017

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