Resolution Width and Cutting Plane Rank Are Incomparable

Authors:
Mark Rhodes
Affiliations:
Department of Computer Science, Durham University, Durham, UK DH1 3LE
Venue:
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Year:
2008

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Abstract

We demonstrate that the Cutting Plane (CP) rank of a polytope defined by a system of inequalities derived from a set of unsatisfiable clauses can be arbitrarily larger than the Resolution width of the clauses, thus demonstrating the two measures are incomparable. More specifically, we show there exists an infinite family of unsatisfiable clauses defined over n茂戮驴茂戮驴, which have constant Resolution width, but, yield polytopes which have CP rank 茂戮驴(log2n).