Algorithms Based on the Treewidth of Sparse Graphs

  • Joachim Kneis
  • Daniel Mölle
  • Stefan Richter
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3787)


We prove that given a graph, one can efficiently find a set of no more than m/5.217 + 1 nodes whose removal yields a partial two-tree. As an application, we immediately get simple algorithms for several problems, including Max-Cut, Max-2-SAT and Max-2-XSAT. All of these take a record-breaking time of O *(2 m/5.217), where m is the number of clauses or edges, while only using polynomial space. Moreover, the existence of the aforementioned node sets implies an upper bound of m/5.217 + 3 on the treewidth of a graph with m edges. Letting go of polynomial space restrictions, this can be improved to a bound of m/5.769 + O(log n) on the pathwidth, leading to algorithms for the above problems that take O *(2 m/5.769) time.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Daniel Mölle
    • 1
  • Stefan Richter
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Computer Science DepartmentRWTH Aachen UniversityFed. Rep. of Germany

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