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

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 ċ (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 1/1-1/2(γ+γ3), 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.

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