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)


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.


Travelling Salesman Problem Travel Salesman Problem Hamilton Cycle Black Vertex Polynomial Factor 
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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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