Reduction tests for the prize-collecting Steiner problem

Abstract

This article introduces a proper redefinition of the concept of bottleneck Steiner distance for the Prize-Collecting Steiner Problem. This allows the application of reduction tests known to be effective on Steiner Problem in Graphs in their full power. Computational experiments attest the effectiveness of the proposed tests.

Networks, uncertainty, applications and a crusade for optimality

“…Reduction Tests Reduction tests for the deterministic PCStT have been implemented in [Canuto et al, 2001, Lucena and Resende, 2004, Ljubić et al, 2006 and [Uchoa, 2007]. It has been demonstrated that the utilization of some of these preprocessing procedures can lead to remarkable improvements of the algorithmic performance.…”

Heuristic Algorithms for Solving the Survivable Problem in the Design of Last Mile Communication Networks

“…Canuto et al [12] described an effective multi-start local search approach based on perturbation of the nodes prizes, where path-relining and variable neighborhood search are used to further improve the obtained solutions. Experiments to reduce the number of nodes and edges that need to be considered in an instance of the PCSTP have been described by Uchoa [14]. And Chapovska et al [13] discuss complexity of and solution methods for several variants of the PCSTP.…”

Further contributions to network optimization

“…Two sessions also were devoted to "Optimal Trees." The first session contained papers describing a dynamic programming approach for solving a single-source minimum cost network flow problem with general nonlinear costs [38], a new formulation for the bounded diameter spanning tree problem [98], the use of blossom inequalities in methods for the degree-constrained minimum spanning tree problem [29], reduction tests for the prize-collecting Steiner tree problem [118], and models for a minimum, nonnecessarily spanning, arborescence problem [32]. The second session contained papers describing a polynomial time algorithm for obtaining a minimum weight connected network with additional distance constraints [75], a paper on how to construct broadcast trees in meshes [30] and two papers that study the minimum energy broadcasting problem in wireless networks [6,124].…”