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Approximation Algorithms for the Minimum Bends Traveling Salesman Problem

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Book cover Integer Programming and Combinatorial Optimization (IPCO 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2081))

Abstract

The problem of traversing a set of points in the order that minimizes the total distance traveled (traveling salesman problem) is one of the most famous and well-studied problems in combinatorial optimiza- tion. In this paper, we introduce the metric of minimizing the number of turns in the tour, given that the input points are in the Euclidean plane. We give approximation algorithms for several variants under this metric. For the general case we give a logarithmic approximation algorithm. For the case when the lines of the tour are restricted to being either horizontal or vertical, we give a 2-approximation algorithm. If we have the further restriction that no two points are allowed to have the same x- or y-coordinate, we give an algorithm that finds a tour which makes at most two turns more than the optimal tour. We also introduce several interesting algorithmic techniques for decomposing sets of points in the Euclidean plane that we believe to be of independent interest.

Research partially supported by NSF Career Award CCR-9624828, NSF Grant EIA- 98-02068, a Dartmouth Fellowship, and an Alfred P. Sloane Foundation Fellowship.

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Authors and Affiliations

  1. Dartmouth College, Department of Computer Science, Hanover, NH 03755-3510, Germany

    Clifford Stein? & David P. Wagner*

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  1. Clifford Stein?
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  2. David P. Wagner*
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Editors and Affiliations

  1. Instituut voor Informatica en Informatiekunde, Universiteit Utrecht, Padualaan 14, 3584, CH Utrecht, The Netherlands

    Karen Aardal

  2. CWI, Kruislaan 413, 1098, SJ Amsterdam, The Netherlands

    Bert Gerards

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© 2001 Springer-Verlag Berlin Heidelberg

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Stein?, C., Wagner*, D.P. (2001). Approximation Algorithms for the Minimum Bends Traveling Salesman Problem. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_32

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  • DOI: https://doi.org/10.1007/3-540-45535-3_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42225-9

  • Online ISBN: 978-3-540-45535-6

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