Approximate Constraint Satisfaction Requires Large LP Relaxations

Siu On Chan; James R. Lee; Prasad Raghavendra; David Steurer

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arXiv · 1309.0563

Approximate Constraint Satisfaction Requires Large LP Relaxations

Siu On Chan·James R. Lee·Prasad Raghavendra·David Steurer

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Abstract

We prove super-polynomial lower bounds on the size of linear programming relaxations for approximation versions of constraint satisfaction problems. We show that for these problems, polynomial-sized linear programs are exactly as powerful as programs arising from a constant number of rounds of the Sherali-Adams hierarchy. In particular, any polynomial-sized linear program for Max Cut has an integrality gap of 1/2 and any such linear program for Max 3-Sat has an integrality gap of 7/8.

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BibTeX RIS

Siu On Chan, James R. Lee, Prasad Raghavendra, David Steurer. 2016-02-08. Approximate Constraint Satisfaction Requires Large LP Relaxations. https://arxiv.org/abs/1309.0563

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