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 ∈ ℕ, which have constant Resolution width, but, yield polytopes which have CP rank Ω(log2 n).
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Rhodes, M. (2008). Resolution Width and Cutting Plane Rank Are Incomparable. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_47
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DOI: https://doi.org/10.1007/978-3-540-85238-4_47
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