TSP on Cubic and Subcubic Graphs

  • Sylvia Boyd
  • René Sitters
  • Suzanne van der Ster
  • Leen Stougie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6655)


We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation, is 4/3. Using polyhedral techniques in an interesting way, we obtain a polynomial-time 4/3-approximation algorithm for this problem on cubic graphs, improving upon Christofides’ 3/2-approximation, and upon the 3/2 − 5/389 ≈ 1.487-approximation ratio by Gamarnik, Lewenstein and Svirdenko for the case the graphs are also 3-edge connected. We also prove that, as an upper bound, the 4/3 conjecture is true for this problem on cubic graphs. For subcubic graphs we obtain a polynomial-time 7/5-approximation algorithm and a 7/5 bound on the integrality gap.


Perfect Matchings Travel Salesman Problem Travel Salesman Problem Hamilton Path Linear Programming Relaxation 
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 2011

Authors and Affiliations

  • Sylvia Boyd
    • 1
  • René Sitters
    • 2
  • Suzanne van der Ster
    • 2
  • Leen Stougie
    • 2
    • 3
  1. 1.School of Information Technology and Engineering (SITE)University of OttawaOttawaCanada
  2. 2.Department of Operations ResearchVU UniversityAmsterdamThe Netherlands
  3. 3.CWIAmsterdamThe Netherlands

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