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On semidefinite programming relaxations for the satisfiability problem

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  • Miguel F. Anjos

Abstract

This paper is concerned with the analysis and comparison of semidefinite programming (SDP) relaxations for the satisfiability (SAT) problem. Our presentation is focussed on the special case of 3-SAT, but the ideas presented can in principle be extended to any instance of SAT specified by a set of boolean variables and a propositional formula in conjunctive normal form. We propose a new SDP relaxation for 3-SAT and prove some of its theoretical properties. We also show that, together with two SDP relaxations previously proposed in the literature, the new relaxation completes a trio of linearly sized relaxations with increasing rank-based guarantees for proving satisfiability. A comparison of the relative practical performances of the SDP relaxations shows that, among these three relaxations, the new relaxation provides the best tradeoff between theoretical strength and practical performance within an enumerative algorithm. Copyright Springer-Verlag 2004

Suggested Citation

  • Miguel F. Anjos, 2004. "On semidefinite programming relaxations for the satisfiability problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 349-367, December.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:3:p:349-367
    DOI: 10.1007/s001860400377
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    Cited by:

    1. Yong Xia & Ying-Wei Han, 2014. "Partial Lagrangian relaxation for the unbalanced orthogonal Procrustes problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 225-237, April.

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