The Travelling Salesman Problem in Bounded Degree Graphs

  • Andreas Björklund
  • Thore Husfeldt
  • Petteri Kaski
  • Mikko Koivisto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)

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.

Keywords

Travelling Salesman Problem Travel Salesman Problem Hamilton Cycle Black Vertex Polynomial Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andreas Björklund
    • 1
  • Thore Husfeldt
    • 1
  • Petteri Kaski
    • 2
  • Mikko Koivisto
    • 2
  1. 1.Department of Computer ScienceLund UniversityLundSweden
  2. 2.Helsinki Institute for Information Technology HIIT, Department of Computer ScienceUniversity of HelsinkiFinland

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