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On Solving MAX-SAT Using Sum of Squares

Author

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  • Lennart Sinjorgo

    (CentER, Department of Econometrics and Operations Research, Tilburg University, 5037 AB Tilburg, Netherlands)

  • Renata Sotirov

    (CentER, Department of Econometrics and Operations Research, Tilburg University, 5037 AB Tilburg, Netherlands)

Abstract

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability (MAX-SAT) problem and weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate (MAX-)2-SAT. Our work shows the potential of SDP also for other satisfiability problems by being competitive with some of the best solvers in the yearly MAX-SAT competition. Our solver combines sum of squares (SOS)–based SDP bounds and an efficient parser within a branch-and-bound scheme. On the theoretical side, we propose a family of semidefinite feasibility problems and show that a member of this family provides the rank-two guarantee. We also provide a parametric family of semidefinite relaxations for MAX-SAT and derive several properties of monomial bases used in the SOS approach. We connect two well-known SDP approaches for (MAX)-SAT in an elegant way. Moreover, we relate our SOS-SDP relaxations for partial MAX-SAT to the known SAT relaxations.

Suggested Citation

  • Lennart Sinjorgo & Renata Sotirov, 2024. "On Solving MAX-SAT Using Sum of Squares," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 417-433, March.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:2:p:417-433
    DOI: 10.1287/ijoc.2023.0036
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    References listed on IDEAS

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    1. Roberto Asín Achá & Robert Nieuwenhuis, 2014. "Curriculum-based course timetabling with SAT and MaxSAT," Annals of Operations Research, Springer, vol. 218(1), pages 71-91, July.
    2. Naomi Graham & Hao Hu & Jiyoung Im & Xinxin Li & Henry Wolkowicz, 2022. "A Restricted Dual Peaceman-Rachford Splitting Method for a Strengthened DNN Relaxation for QAP," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2125-2143, July.
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