A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Disjunctive programming: properties of the convex hull of feasible points
Discrete Applied Mathematics
On a Representation of the Matching Polytope Via Semidefinite Liftings
Mathematics of Operations Research
When Does the Positive Semidefiniteness Constraint Help in Lifting Procedures?
Mathematics of Operations Research
SIAM Journal on Optimization
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Matrix-Cut Rank of Polyhedra
Mathematics of Operations Research
Lift and project relaxations for the matching and related polytopes
Discrete Applied Mathematics
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Subset Algebra Lift Operators for 0-1 Integer Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
Computation of the Lasserre Ranks of Some Polytopes
Mathematics of Operations Research
Discrete Applied Mathematics
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
Theta Bodies for Polynomial Ideals
SIAM Journal on Optimization
On integrality ratios for asymmetric TSP in the sherali-adams hierarchy
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Many hierarchies of lift-and-project relaxations for 0,1 integer programs have been proposed, two of the most recent and strongest being those by Lasserre in 2001, and Bienstock and Zuckerberg in 2004. We prove that, on the LP relaxation of the matching polytope of the complete graph on (2n+1) vertices defined by the nonnegativity and degree constraints, the Bienstock-Zuckerberg operator (even with positive semidefiniteness constraints) requires Θ(√n) rounds to reach the integral polytope, while the Lasserre operator requires Θ(n) rounds. We also prove that Bienstock-Zuckerberg operator, without the positive semidefiniteness constraint requires approximately n/2 rounds to reach the stable set polytope of the n-clique, if we start with the fractional stable set polytope. As a by-product of our work, we consider a significantly strengthened version of Sherali-Adams operator and a strengthened version of Bienstock-Zuckerberg operator. Most of our results also apply to these stronger operators.