Rank Lower Bounds for the Sherali-Adams Operator

Authors:
Mark Rhodes
Affiliations:
Durham University, Department of Computer Science, South Road, Durham, Co. Durham, DH1 3LE, UK
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

Citing 2
Cited 2

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A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming

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Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems

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Resolution Width and Cutting Plane Rank Are Incomparable

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Abstract

We consider the Sherali-Adams (SA) operator as a proof system for integer linear programming and prove linear lower bounds on the SA rank required to prove both the pigeon hole and least number principles. We also define the size of a SA proof and show that that while the pigeon hole principle requires linear rank, it only requires at most polynomial size.