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Resolution Branch and Bound and an Application: The Maximum Weighted Stable Set Problem

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  • Alessandro Avenali

    (Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza,” 00185 Roma, Italy)

Abstract

We propose a new resolution algorithm, called resolution branch and bound (RBB), where a branch-and-bound scheme is empowered by exploiting the information contained in a family of closed subproblems, collected by a full resolution phase. In particular, we use this information to define a new branching rule that seems able to reduce the risk of incurring inappropriate branchings. We apply RBB and the proposed branching rule to the maximum weighted stable set problem, as its features allow us to speed up a time-consuming step in the full resolution phase. To compute upper bounds, we generalize to the weighted case the polynomial time procedure provided by Mannino and Sassano [Mannino, C., A. Sassano. 1994. An exact algorithm for the maximum stable set problem. Computational Optim. Appl. 3 243--258] for the unweighted case. Computational results validate the effectiveness of the provided branching rule and the good performance of RBB on many DIMACS benchmarks.

Suggested Citation

  • Alessandro Avenali, 2007. "Resolution Branch and Bound and an Application: The Maximum Weighted Stable Set Problem," Operations Research, INFORMS, vol. 55(5), pages 932-948, October.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:5:p:932-948
    DOI: 10.1287/opre.1070.0397
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    Cited by:

    1. Steffen Rebennack & Marcus Oswald & Dirk Oliver Theis & Hanna Seitz & Gerhard Reinelt & Panos M. Pardalos, 2011. "A Branch and Cut solver for the maximum stable set problem," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 434-457, May.
    2. Alessandro Avenali & Giorgio Matteucci & Fabio Nonino, 2010. "Outsourcing of Facility Management Activities and Procurement Design," DIS Technical Reports 2010-13, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".

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