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Polynomial-time separation of simple comb inequalities

Research output: Working paper


Publication date2003
Place of publicationLancaster University
PublisherThe Department of Management Science
Number of pages0
<mark>Original language</mark>English

Publication series

NameManagement Science Working Paper Series


The comb inequalities are a well-known class of facet-inducing inequalities for the Travelling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds, and also the so-called Chvatal comb inequalities. In 1982, Padberg and Rao [29] gave a polynomial-time algorithm for separating the 2-matching inequalities - i.e., for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time algorithm for separating the simple comb inequalities. The key is a result due to Caprara and Fischetti.

Bibliographic note

This was eventually published as: L.K. Fleischer, A.N. Letchford & A. Lodi (2006) Polynomial-time separation of a superclass of simple comb inequalities. Math. Oper. Res., 31(4), 696-713.

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