Abstract
We show improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs. For cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi [10] by giving a “local improvement” algorithm that finds a tour of length at most \(5/4n-2\). For 2-connected cubic graphs, we show that the techniques of Mömke and Svensson [11] can be combined with the techniques of Correa et al. [6], to obtain a tour of length at most \((4/3-1/8754)n\).
A. van Zuylen—This work was supported by a grant from the Simons Foundation (#359525, Anke Van Zuylen) and by NSF Prime Award: HRD-1107147, Women in Scientific Education (WISE).
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Acknowledgements
The author would like to thank Marcin Mucha for careful reading and pointing out an omission in a previous version, Frans Schalekamp for helpful discussions, and an anonymous reviewer for suggesting the simplified proof for the result in Sect. 3 for cubic non-bipartite graphs. Other anonymous reviewers are acknowledged for helpful feedback on the presentation of the algorithm for bipartite cubic graphs.
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van Zuylen, A. (2016). Improved Approximations for Cubic Bipartite and Cubic TSP. In: Louveaux, Q., Skutella, M. (eds) Integer Programming and Combinatorial Optimization. IPCO 2016. Lecture Notes in Computer Science(), vol 9682. Springer, Cham. https://doi.org/10.1007/978-3-319-33461-5_21
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