Fast subexponential algorithm for non-local problems on graphs of bounded genus

  • Authors:

  • Frederic Dorn;Fedor V. Fomin;Dimitrios M. Thilikos

  • Affiliations:

  • Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway;Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Barcelona, Spain

  • Venue:
  • SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
  • Year:
  • 2006

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Abstract

We give a general technique for designing fast subexponential algorithms for several graph problems whose instances are restricted to graphs of bounded genus. We use it to obtain time $2^{O(\sqrt{n})}$ algorithms for a wide family of problems such as Hamiltonian Cycle, Σ-embedded Graph Travelling Salesman Problem, Longest Cycle, and Max Leaf Tree. For our results, we combine planarizing techniques with dynamic programming on special type branch decompositions. Our techniques can also be used to solve parameterized problems. Thus, for example, we show how to find a cycle of length p (or to conclude that there is no such a cycle) on graphs of bounded genus in time $2^{O( \sqrt{p})}\cdot n^{O(1)}$