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A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem

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Principles and Practice of Constraint Programming – CP 2003 (CP 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2833))

Abstract

This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.

An earlier version of this paper appeared as [18].

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Authors and Affiliations

  1. CWI, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands

    Willem Jan van Hoeve

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  1. Willem Jan van Hoeve
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  1. Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Francesca Rossi

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van Hoeve, W.J. (2003). A Hybrid Constraint Programming and Semidefinite Programming Approach for the Stable Set Problem. In: Rossi, F. (eds) Principles and Practice of Constraint Programming – CP 2003. CP 2003. Lecture Notes in Computer Science, vol 2833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45193-8_28

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  • DOI: https://doi.org/10.1007/978-3-540-45193-8_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20202-8

  • Online ISBN: 978-3-540-45193-8

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