Improved approximations for cubic bipartite and cubic TSP
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We show improved approximation guarantees for the traveling salesman problem on cubic bipartite graphs and cubic graphs. For connected cubic bipartite graphs with n nodes, we improve on recent results of Karp and Ravi 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 can be combined with the techniques of Correa, Larré and Soto, to obtain a tour of length at most \((4/3-1/8754)n\).
KeywordsTraveling salesman problem Approximation algorithm Cubic bipartite graphs Cubic graphs Barnette’s conjecture
Mathematics Subject Classification68W25 approximation algorithms 68W40 analysis of algorithms 05C85 graph algorithms
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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