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The Travelling Salesman Problem in Bounded Degree Graphs

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Automata, Languages and Programming (ICALP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5125))

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Abstract

We show that the travelling salesman problem in bounded-degree graphs can be solved in time \(O\bigl((2-\epsilon)^n\bigr)\), where ε> 0 depends only on the degree bound but not on the number of cities, n. The algorithm is a variant of the classical dynamic programming solution due to Bellman, and, independently, Held and Karp. In the case of bounded integer weights on the edges, we also present a polynomial-space algorithm with running time \(O\bigl((2-\epsilon)^n\bigr)\) on bounded-degree graphs.

This research was supported in part by the Swedish Research Council, project “Exact Algorithms” (A.B., T.H.), and the Academy of Finland, Grants 117499 (P.K.) and 109101 (M.K.).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Lund University, P.O.Box 118, SE-22100, Lund, Sweden

    Andreas Björklund & Thore Husfeldt

  2. Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, P.O.Box 68, FI-00014, Finland

    Petteri Kaski & Mikko Koivisto

Authors
  1. Andreas Björklund
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  2. Thore Husfeldt
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  3. Petteri Kaski
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  4. Mikko Koivisto
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Editor information

Editors and Affiliations

  1. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Luca Aceto

  2. Department of Computer Science, IT-Parken, University of Aarhus, Åbogade 34, 8200, ÅrhusN, Denmark

    Ivan Damgård

  3. Department of Computer Science, University of Liverpool, Ashton Building, L69 3BX, Liverpool, UK

    Leslie Ann Goldberg

  4. School of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavik, Iceland

    Magnús M. Halldórsson

  5. Department of Computer Science, Reykjavik University, Kringlan 1, 103, Reykjavík, Iceland

    Anna Ingólfsdóttir

  6. Université de Bordeaux-1, LaBRI, 351, Cours de la Libération, 33405, Talence cedex, France

    Igor Walukiewicz

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Björklund, A., Husfeldt, T., Kaski, P., Koivisto, M. (2008). The Travelling Salesman Problem in Bounded Degree Graphs . In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds) Automata, Languages and Programming. ICALP 2008. Lecture Notes in Computer Science, vol 5125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70575-8_17

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  • DOI: https://doi.org/10.1007/978-3-540-70575-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-70574-1

  • Online ISBN: 978-3-540-70575-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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