Approximate Constraint Satisfaction Requires Large LP Relaxations
2013 IEEE 54TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS)（2016）
摘要
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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关键词
approximation complexity,large lp relaxations,polynomial-sized linear program,integrality gap,max cut,approximate constraint satisfaction,max 3-sat,approximation version,constraint satisfaction problem,sherali-adams hierarchy,superpolynomial lower bounds,approximate constraint satisfaction problem,extended formulations,linear programming,lp hierarchies,constraint satisfaction problems,polynomial-sized linear programs,computational complexity,computability,lower bounds,lp relaxation,linear programming relaxations,linear program,graph theory,constant number,linear programming relaxation
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