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Traveling Salesman Problem of Segments

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Book cover Computing and Combinatorics (COCOON 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2697))

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Abstract

In this paper, we present a polynomial time approximation scheme (PTAS) for a variant of the traveling salesman problem (called segment TSP) in which a traveling salesman tour is sought to traverse a set of n ∈-separated segments in two dimensional space. Our results are based on a number of geometric observations and an interesting generalization of Arora’s technique 5 for Euclidean TSP (of a set of points). The randomized version of our algorithm takes \( O(n^2 (\log n)^{O(1/\varepsilon ^4 )} ) \) time to compute a (1 + ∈)-approximation with probability ≥ 1/2, and can be derandomized with an additional factor of O(n 2). Our technique is likely applicable to TSP problems of certain Jordan arcs and related problems.

This research was supported in part by an IBM faculty partnership award, and an award from NYSTAR (New York state office of science, technology, and academic research) through MDC (Microelectronics Design Center).

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, State University of New York at Buffalo, Buffalo, NY, 14260, USA

    Jinhui Xu, Yang Yang & Zhiyong Lin

Authors
  1. Jinhui Xu
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  2. Yang Yang
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  3. Zhiyong Lin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Austin, One University Station, C0500, Austin, TX, 78712, USA

    Tandy Warnow

  2. Department of Computer Science, Montana State University, EPS 357, Bozeman, MT, 59717, USA

    Binhai Zhu

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© 2003 Springer-Verlag Berlin Heidelberg

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Xu, J., Yang, Y., Lin, Z. (2003). Traveling Salesman Problem of Segments. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_6

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  • DOI: https://doi.org/10.1007/3-540-45071-8_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40534-4

  • Online ISBN: 978-3-540-45071-9

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