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Sum-of-squares rank upper bounds for matching problems

Author

Listed:
  • Adam Kurpisz

    (IDSIA)

  • Samuli Leppänen

    (IDSIA)

  • Monaldo Mastrolilli

    (IDSIA)

Abstract

The matching problem is one of the most studied combinatorial optimization problems in the context of extended formulations and convex relaxations. In this paper we provide upper bounds for the rank of the sum-of-squares/Lasserre hierarchy for a family of matching problems. In particular, we show that when the problem formulation is strengthened by incorporating the objective function in the constraints, the hierarchy requires at most $$\left\lceil \frac{k}{2} \right\rceil $$ k 2 levels to refute the existence of a perfect matching in an odd clique of size $$2k+1$$ 2 k + 1 .

Suggested Citation

  • Adam Kurpisz & Samuli Leppänen & Monaldo Mastrolilli, 2018. "Sum-of-squares rank upper bounds for matching problems," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 831-844, October.
    • Handle: RePEc:spr:jcomop:v:36:y:2018:i:3:d:10.1007_s10878-017-0169-2
    DOI: 10.1007/s10878-017-0169-2
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    References listed on IDEAS

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    1. Monique Laurent, 2003. "A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 470-496, August.
    2. Michel X. Goemans & Levent Tunçel, 2001. "When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 796-815, November.
    3. Pratik Worah, 2015. "Rank bounds for a hierarchy of Lovász and Schrijver," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 689-709, October.
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