A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Complexity of Semi-algebraic Proofs
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
A Study of Proof Search Algorithms for Resolution and Polynomial Calculus
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A comparison of the Sherali-Adams, Lov\'\'\'\'341sz-Schrijver and Lasserre relaxations for 0-1 programming
Towards strong nonapproximability results in the Lovasz-Schrijver hierarchy
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
| Hi-index | 5.23 |
We consider a proof (more accurately, refutation) system based on the Sherali-Adams (SA) operator associated with integer linear programming. If F is a CNF contradiction that admits a Resolution refutation of width k and size s, then we prove that the SA rank of F is @?k and the SA size of F is @?(k+1)s+1. We establish that the SA rank of both the Pigeonhole Principle PHP"n"-"1^n and the Least Number Principle LNP"n is n-2. Since the SA refutation system rank-simulates the refutation system of Lovasz-Schrijver without semidefinite cuts (LS), we obtain as a corollary linear rank lower bounds for both of these principles in LS.