Polynomial-Time Separation of a Superclass of Simple Comb Inequalities

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 Chvátal comb inequalities.

In 1982, Padberg and Rao [34] 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 a class of valid inequalities which includes all simple comb inequalities.

By: Lisa K. Fleischer, Adam N. Letchford, Andrea Lodi

Published in: RC23250 in 2004


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to reports@us.ibm.com .