Optimal Sherali-Adams Gaps from Pairwise Independence

  • Konstantinos Georgiou
  • Avner Magen
  • Madhur Tulsiani
Conference paper

DOI: 10.1007/978-3-642-03685-9_10

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5687)
Cite this paper as:
Georgiou K., Magen A., Tulsiani M. (2009) Optimal Sherali-Adams Gaps from Pairwise Independence. In: Dinur I., Jansen K., Naor J., Rolim J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg

Abstract

This work considers the problem of approximating fixed predicate constraint satisfaction problems (MAX k-CSP(P)). We show that if the set of assignments accepted by P contains the support of a balanced pairwise independent distribution over the domain of the inputs, then such a problem on n variables cannot be approximated better than the trivial (random) approximation, even using Ω(n) levels of the Sherali-Adams LP hierarchy.

It was recently shown [3] that under the Unique Game Conjecture, CSPs with predicates with this condition cannot be approximated better than the trivial approximation. Our results can be viewed as an unconditional analogue of this result in the restricted computational model defined by the Sherali-Adams hierarchy. We also introduce a new generalization of techniques to define consistent “local distributions” over partial assignments to variables in the problem, which is often the crux of proving lower bounds for such hierarchies.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Konstantinos Georgiou
    • 1
  • Avner Magen
    • 1
  • Madhur Tulsiani
    • 2
  1. 1.Department of Computer ScienceUniversity of TorontoCanada
  2. 2.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA

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