Separating clique tree and bipartition inequalities in polynomial time

Abstract

Many important cutting planes have been discovered for the traveling salesman problem. Among them are the clique tree inequalities and the more general bipartition inequalities. Little is known in the way of exact algorithms for separating these inequalities in polynomial time in the size of the fractional point X ^* which is being separated. An algorithm is presented here that separates bipartition inequalities of a fixed number of handles and teeth, which includes clique tree inequalities of a fixed number of handles and teeth, in polynomial time.