On the complexity of cutting-plane proofs
Discrete Applied Mathematics
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Rank Bounds and Integrality Gaps for Cutting Planes Procedures
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Rank Lower Bounds for the Sherali-Adams Operator
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Tight rank lower bounds for the Sherali–Adams proof system
Theoretical Computer Science
Note: On the Chvátal rank of the Pigeonhole Principle
Theoretical Computer Science
Cutting Planes and the Parameter Cutwidth
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
The limits of tractability in resolution-based propositional proof systems
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
On the rank of cutting-plane proof systems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Hi-index | 0.00 |
We prove a dichotomy theorem for the rank of the uniformly generated(i.e. expressible in First-Order (FO) Logic) propositional tautologiesin both the Lovász-Schrijver (LS) and Sherali-Adams (SA) proofsystems. More precisely, we first show that the propositional translationsof FO formulae that are universally true, i.e. hold in all finiteand infinite models, have LS proofs whose rank is constant, independentlyfrom the size of the (finite) universe. In contrast to that, we provethat the propositional formulae that hold in all finite models butfail in some infinite structure require proofs whose SA rank grows poly-logarithmically with the size of the universe. Up to now, this kind of so-called "Complexity Gap" theorems have been known for Tree-like Resolution and, in somehow restrictedforms, for the Resolution and Nullstellensatz proof systems. As faras we are aware, this is the first time the Sherali-Adams lift-and-projectmethod has been considered as a propositional proof system. An interesting feature of the SA proof system is that it is static and rank-preserving simulates LS, the Lovász-Schrijver proof system without semidefinitecuts.