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Edge-swapping algorithms for the minimum fundamental cycle basis problem

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  • Edoardo Amaldi
  • Leo Liberti
  • Francesco Maffioli
  • Nelson Maculan

Abstract

We consider the problem of finding a fundamental cycle basis with minimum total cost in an undirected graph. This problem is NP-hard and has several interesting applications. Since fundamental cycle bases correspond to spanning trees, we propose a local search algorithm, a tabu search and variable neighborhood search in which edge swaps are iteratively applied to a current spanning tree. We also present a mixed integer programming formulation of the problem whose linear relaxation yields tighter lower bounds than other known formulations. Computational results obtained with our algorithms are compared with those from the best available constructive heuristic on several types of graphs. Copyright Springer-Verlag 2009

Suggested Citation

  • Edoardo Amaldi & Leo Liberti & Francesco Maffioli & Nelson Maculan, 2009. "Edge-swapping algorithms for the minimum fundamental cycle basis problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 205-233, May.
    • Handle: RePEc:spr:mathme:v:69:y:2009:i:2:p:205-233
    DOI: 10.1007/s00186-008-0255-4
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    References listed on IDEAS

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    1. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
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    1. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.
    2. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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