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Dynamic Programming on Tree Decompositions Using Generalised Fast Subset Convolution

  • Johan M. M. van Rooij
  • Hans L. Bodlaender
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5757)

Abstract

In this paper, we show that algorithms on tree decompositions can be made faster with the use of generalisations of fast subset convolution. Amongst others, this gives algorithms that, for a graph, given with a tree decomposition of width k, solve the dominated set problem in O(n k 2 3 k ) time and the problem to count the number of perfect matchings in O  ∗ (2 k ) time. Using a generalisation of fast subset convolution, we obtain faster algorithms for all [ρ,σ]-domination problems with finite or cofinite ρ and σ on tree decompositions. These include many well known graph problems. We give additional results on many more graph covering and partitioning problems.

Keywords

Dynamic Programming Planar Graph Partial Solution Dynamic Programming Algorithm Tree Decomposition 
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 2009

Authors and Affiliations

  • Johan M. M. van Rooij
    • 1
  • Hans L. Bodlaender
    • 1
  • Peter Rossmanith
    • 2
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Computer Science DepartmentRWTH Aachen UniversityAachenGermany

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