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In this article, we investigate the stochastic maximum weight forest problem. We present two mathematical formulations for the problem: a polynomial sized one based on the characterization of forests in graphs and a formulation with an exponential number of constraints. We give a proof of the correctness of the new formulation and present a polynomial reduction from the set cover problem to give some...
We introduce the class of spot‐checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. Although SC games are not zero‐sum, we show that a Nash equilibrium can be computed...
The reload cost spanning tree problem (RCSTP) is an NP‐hard problem, where we are given a set of nonnegative pairwise demands between nodes, each edge is colored and a reload cost is incurred when a color change occurs on the path between a pair of demand nodes. The goal is to find a spanning tree with minimum total reload cost. We propose a tree–nontree edge swap neighborhood for the RCSTP and an...
The quadratic minimum spanning tree problem (QMSTP) consists of finding a spanning tree of a graph G such that a quadratic cost function is minimized. In its adjacent only version (AQMSTP), interaction costs only apply for edges that share an endpoint. Motivated by the weak lower bounds provided by formulations in the literature, we present a new linear integer programming formulation for AQMSTP....
In telecommunication networks, packets are carried from a source to a destination on a path determined by the underlying routing protocol. Most routing protocols belong to the class of shortest path routing protocols. In such protocols, the network operator assigns a length to each link. A packet going from to follows a shortest path according to these lengths. For better protection and...
We study the incremental facility location problem, wherein we are given an instance of the uncapacitated facility location problem (UFLP) and seek an incremental sequence of opening facilities and an incremental sequence of serving customers along with their fixed assignments to facilities open in the partial sequence. We say that a sequence has a competitive ratio of k, if the cost of serving the...
Given a connected and undirected graph G, the degree preserving spanning tree problem (DPSTP) asks for a spanning tree of G with the maximum number of vertices having the same degree in the tree and in G. These are called full degree vertices. We introduce integer programming formulations, valid inequalities and four exact solution approaches based on different formulations. Two branch‐and‐bound procedures,...
In this article, we study the (k,c)‐coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c colors. We propose a new formulation for the (k,c)‐coloring problem and develop a Branch‐and‐Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and...
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