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Differential Approximation Results for the Traveling Salesman Problem with Distances 1 and 2

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Fundamentals of Computation Theory (FCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2138))

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Abstract

We prove that both minimum and maximum traveling salesman problems on complete graphs with edge-distances 1 and 2 are approximable within 3/4. Based upon this result, we improve the standard approximation ratio known for maximum traveling salesman with distances 1 and 2 from 3/4 to 7/8. Finally, we prove that, for any ε > 0, it is NP-hard to approximate both problems within better than 5379/5380 + ε.

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Author information

Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775, Paris Cedex 16, France

    Jérôme Monnot, Vangelis T. Paschos & Sophie Toulouse

Authors
  1. Jérôme Monnot
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  2. Vangelis T. Paschos
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  3. Sophie Toulouse
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Editor information

Editors and Affiliations

  1. University of Latvia, Raiņa bulvaris 29, LV-1459, Riga, Latvia

    Rūsiņš Freivalds

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© 2001 Springer-Verlag Berlin Heidelberg

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Monnot, J., Paschos, V.T., Toulouse, S. (2001). Differential Approximation Results for the Traveling Salesman Problem with Distances 1 and 2. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_27

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  • DOI: https://doi.org/10.1007/3-540-44669-9_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42487-1

  • Online ISBN: 978-3-540-44669-9

  • eBook Packages: Springer Book Archive

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