Letchford, A N and Lodi, A (2003) Polynomial-time separation of simple comb inequalities. Working Paper. The Department of Management Science, Lancaster University.Full text not available from this repository.
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  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.
|Item Type:||Monograph (Working Paper)|
|Additional Information:||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.|
|Uncontrolled Keywords:||travelling salesman problem ; cutting planes ; separation|
|Departments:||Lancaster University Management School > Management Science|
|Deposited On:||11 Jul 2011 22:04|
|Last Modified:||27 Jul 2012 01:11|
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