An Improved Approximation Algorithm for the Asymmetric TSP with Strengthened Triangle Inequality

Abstract

We consider the asymmetric traveling salesperson problem with γ-parameterized triangle inequality for γ ∈ [1/2, 1). That means, the edge weights fulfill w(u, v) ≤ γ · (w(u, x) + w(x, v)) for all nodes u, v, x. Chandran and Ram [6] recently gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio γ/1−γ. We devise an approximation algorithm with performance ratio \( \frac{1} {{1 - \frac{1} {2}\left( {\gamma + \gamma ^3 } \right)}} \), which is better than the one by Chandran and Ram for γ ∈ [0.6507, 1), that is, for the particularly interesting large values of γ.