Approximations for ATSP with parametrized triangle inequality

Abstract

We gve a constant factor (Formula present) approximation for the asymmetric traveling salesman problem in graphs with costs on the edges satisfying γ-parametrized triangle inequality (γ-Asymmetric graphs) for γ ∈ [1/2, 1). We also give an improvement of the algorithm with approximation factor approaching γ/1-γ. We also explore the cmax/cmin ratio of edge costs in a general asymmetric graph. We show that for γ ∈ (Formula present), cmax/cmin ≤ (Formula present), while for γ ∈ (Formula present), this ratio can be arbitrarily large. We make use of this result to give a better analysis to our main algorithm. We also observe that when cmax/cmin > (Formula present), the minimum cost and the maximum cost edges in the graph are unique and are reverse to each other. © Springer-Verlag Berlin Heidelberg 2002.