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On Labeled Traveling Salesman Problems

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Algorithms and Computation (ISAAC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5369))

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Abstract

We consider labeled Traveling Salesman Problems, defined upon a complete graph of n vertices with colored edges. The objective is to find a tour of maximum (or minimum) number of colors. We derive results regarding hardness of approximation, and analyze approximation algorithms for both versions of the problem. For the maximization version we give a \(\frac{1}{2}\)-approximation algorithm and show that it is APX-hard. For the minimization version, we show that it is not approximable within n 1 − ε for every ε> 0. When every color appears in the graph at most r times and r is an increasing function of n the problem is not O(r 1 − ε)-approximable. For fixed constant r we analyze a polynomial-time (r + H r )/2-approximation algorithm (H r is the r-th harmonic number), and prove APX-hardness. Analysis of the studied algorithms is shown to be tight.

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Author information

Authors and Affiliations

  1. CNRS UMR 7024 LAMSADE, Université de Paris-Dauphine, France

    Basile Couëtoux, Laurent Gourvès & Jérôme Monnot

  2. Department of Computer Science, University of Aarhus, Denmark

    Orestis A. Telelis

Authors
  1. Basile Couëtoux
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  2. Laurent Gourvès
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  3. Jérôme Monnot
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  4. Orestis A. Telelis
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Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  2. Graduate School of Informatics, Kyoto University, 606-8501, Kyoto, Japan

    Hiroshi Nagamochi

  3. Graduate School of Informatics, Kyoto University, Japan

    Takuro Fukunaga

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© 2008 Springer-Verlag Berlin Heidelberg

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Couëtoux, B., Gourvès, L., Monnot, J., Telelis, O.A. (2008). On Labeled Traveling Salesman Problems. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_68

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  • DOI: https://doi.org/10.1007/978-3-540-92182-0_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92181-3

  • Online ISBN: 978-3-540-92182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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