Improved Approximations for Cubic Bipartite and Cubic TSP

Conference paper

DOI: 10.1007/978-3-319-33461-5_21

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9682)
Cite this paper as:
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

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 \((4/3-1/8754)n\).

Keywords

Traveling salesman problem Approximation algorithm Cubic bipartite graphs Cubic graphs Barnette’s conjecture 

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsCollege of William & MaryWilliamsburgUSA

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