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Finding Branch-Decompositions and Rank-Decompositions

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Algorithms – ESA 2007 (ESA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4698))

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Abstract

We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parameter tractable, that is, they run in time O(n 3) for each fixed value of k where n is the number of vertices / elements of the input. (The previous best algorithm for construction of a branch-decomposition or a rank-decomposition of optimal width due to Oum and Seymour [Testing branch-width. J. Combin. Theory Ser. B, 97(3) (2007) 385–393] is not fixed-parameter tractable).

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, 602 00 Brno, Czech Republic

    Petr Hliněný

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

    Sang-il Oum

Authors
  1. Petr Hliněný
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  2. Sang-il Oum
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Editor information

Lars Arge Michael Hoffmann Emo Welzl

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© 2007 Springer-Verlag Berlin Heidelberg

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Hliněný, P., Oum, Si. (2007). Finding Branch-Decompositions and Rank-Decompositions. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_16

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  • DOI: https://doi.org/10.1007/978-3-540-75520-3_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75519-7

  • Online ISBN: 978-3-540-75520-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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