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The generalized minimum spanning tree problem: Polyhedral analysis and branch‐and‐cut algorithm
Author(s) -
Feremans Corinne,
Labbé Martine,
Laporte Gilbert
Publication year - 2004
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.10105
Subject(s) - minimum spanning tree , steiner tree problem , spanning tree , branch and cut , k minimum spanning tree , tabu search , vertex (graph theory) , mathematics , integer programming , combinatorics , kruskal's algorithm , euclidean geometry , heuristic , algorithm , graph , mathematical optimization , tree structure , k ary tree , binary tree , geometry
This article presents a branch‐and‐cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose vertex set is partitioned into clusters, the GMSTP consists of determining a minimum‐cost tree including exactly one vertex per cluster. Applications of the GMSTP are encountered in telecommunications. An integer linear programming formulation is presented and new classes of valid inequalities are developed, several of which are proved to be facet‐defining. A branch‐and‐cut algorithm and a tabu search heuristic are developed. Extensive computational experiments show that instances involving up to 160 or 200 vertices can be solved to optimality, depending on whether edge costs are Euclidean or random. © 2004 Wiley Periodicals, Inc.