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From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization

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Fundamentals of Computation Theory (FCT 2021)

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Abstract

We generalize the tree doubling and Christofides algorithm to parameterized approximations for ATSP. The parameters we consider for the respective generalizations are upper bounded by the number of asymmetric distances, which yields algorithms to efficiently compute good approximations also for moderately asymmetric TSP instances. As generalization of the Christofides algorithm, we derive a parameterized 2.5-approximation, where the parameter is the size of a vertex cover for the subgraph induced by the asymmetric distances. Our generalization of the tree doubling algorithm gives a parameterized 3-approximation, where the parameter is the minimum number of asymmetric distances in a minimum spanning arborescence. Further, we combine these with a notion of symmetry relaxation which allows to trade approximation guarantee for runtime. Since the two parameters we consider are theoretically incomparable, we present experimental results which show that generalized tree doubling frequently outperforms generalized Christofides with respect to parameter size.

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Notes

  1. 1.

    https://github.com/Blaidd-Drwg/atsp-approximation.

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Correspondence to Katrin Casel .

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Behrendt, L., Casel, K., Friedrich, T., Gregor Lagodzinski, J.A., Löser, A., Wilhelm, M. (2021). From Symmetry to Asymmetry: Generalizing TSP Approximations by Parametrization. In: Bampis, E., Pagourtzis, A. (eds) Fundamentals of Computation Theory. FCT 2021. Lecture Notes in Computer Science(), vol 12867. Springer, Cham. https://doi.org/10.1007/978-3-030-86593-1_4

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