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The Traveling Salesman Problem for Cubic Graphs

  • David Eppstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)

Abstract

We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time \(\mathcal{O}(2^{n/3}) \approx {\rm 1.25992}^n\) and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound, and count the number of Hamiltonian cycles in time \(\mathcal{O}(2^{3n/8}n^{\mathcal{O}(1)}) \approx {\rm 1.29684}^n\). We also solve the traveling salesman problem in graphs of degree at most four, by a randomized (Monte Carlo) algorithm with runtime \(\mathcal{O}((27/4)^{n/3}) \approx {\rm 1.88988}^n\). Our algorithms allow the input to specify a set of forced edges which must be part of any generated cycle.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • David Eppstein
    • 1
  1. 1.School of Information & Computer ScienceUniversity of California, IrvineIrvineUSA

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