Approximating the bipartite TSP and its biased generalization

Abstract

We examine a generalization of the symmetric bipartite traveling salesman problem (TSP) with quadrangle inequality, by extending the cost function of a Hamiltonian tour to include a bias factor β ≥ 1. The bias factor is known and given as a part of the input. We propose a novel heuristic procedure for building Hamiltonian cycles in bipartite graphs, and show that it is an approximation algorithm for the generalized problem with an approximation ratio of, where λ is a real parameter dependent on the problem instance. This expression is bounded above by a constant 2, for any positive real λ and β ≥ 1, which improves a previously reported approximation ratio of 16/7. As a part of a composite heuristic, the proposed procedure can contribute to an approximation ratio of, where ζ is an approximation ratio for the metric TSP. © 2014 Springer International Publishing Switzerland.