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A branch-and-cut algorithm for the maximum covering cycle problem

Author

Listed:
  • Eduardo Álvarez-Miranda

    (Universidad de Talca)

  • Markus Sinnl

    (University of Vienna)

Abstract

In many applications, such as telecommunications and routing, we seek for cost-effective infrastructure or operating layouts so that many nodes (e.g., customers) of a support network (typically modeled by a graph) are covered by, or at least are easily reachable from, such a layout. In this paper, we study the maximum covering cycle problem. In this problem we are given a non-complete graph, and the goal is to find a cycle, such that the number of nodes which are either on the cycle or are adjacent to the cycle is maximized. We design a branch-and-cut framework for solving the problem. The framework contains valid inequalities, lifted inequalities and a primal heuristic. In a computational study, we compare our framework to previous work available for this problem. The results reveal that our approach significantly outperforms the previous approach. In particular, all available instances from the literature could be solved to optimality with our approach, most of them within a few seconds.

Suggested Citation

  • Eduardo Álvarez-Miranda & Markus Sinnl, 2020. "A branch-and-cut algorithm for the maximum covering cycle problem," Annals of Operations Research, Springer, vol. 284(2), pages 487-499, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:2:d:10.1007_s10479-018-2856-5
    DOI: 10.1007/s10479-018-2856-5
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    References listed on IDEAS

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