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.
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Bläser, M. (2003). An Improved Approximation Algorithm for the Asymmetric TSP with Strengthened Triangle Inequality. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_14
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DOI: https://doi.org/10.1007/3-540-45061-0_14
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