An Improved Exact Algorithm for Cubic Graph TSP

  • Kazuo Iwama
  • Takuya Nakashima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4598)


It is shown that the traveling salesman problem for graphs of degree at most three with n vertices can be solved in time O(1.251 n ), improving the previous bound O(1.260 n ) by Eppstein.


Planar Graph Minimum Span Tree Travel Salesman Problem Hamiltonian Cycle Free Vertex 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. SIAM Journal on Applied Mathematics 10, 196–210 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)zbMATHGoogle Scholar
  3. 3.
    Lipton, R.J., Tarjan, R.E.: A separator theorem for planar graphs. SIAM Journal on Applied Mathematics 36, 177–189 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Lipton, R.J., Tarjan, R.E.: Applications of a planar separator theorem. SIAM Journal on Computing 9, 615–627 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hwang, R.Z., Chang, R.C., Lee, R.C.T.: The Searching over Separators Strategy To Solve Some NP-Hard Problems in Subexponential Time. Algorithmica 9, 398–423 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Iwama, K., Tamaki, S.: Improved Upper Bounds for 3-SAT, 15th annual ACM-SIAM Symposium on Discrete Algorithms. In: Proc. SODA, January 2004, pp. 328–329 (2004)Google Scholar
  7. 7.
    Woeginger, G.J.: Exact Algorithms for NP-Hard Problems: A Survey. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.) Combinatorial Optimization - Eureka, You Shrink! LNCS, vol. 2570, pp. 185–207. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Eppstein, D.: The Traveling Salesman Problem for Cubic Graphs. In: Dehne, F., Sack, J.-R., Smid, M. (eds.) WADS 2003. LNCS, vol. 2748, pp. 307–318. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Dorn, F., Penninkx, E., Bodlaender, H.L., Fomin, F.V.: Efficient Exact Algorithms on Planar Graphs:Exploiting Sphere Cut Branch Decompositions. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 95–106. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Kazuo Iwama
    • 1
  • Takuya Nakashima
    • 1
  1. 1.School of Informatics, Kyoto University, Kyoto 606-8501Japan

Personalised recommendations