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Approximating treewidth and pathwidth of some classes of perfect graphs

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Algorithms and Computation (ISAAC 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 650))

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Abstract

In this paper we discuss algorithms that approximate the treewidth and pathwidth of cotriangulated graphs, permutation graphs and of cocomparability graphs. For a cotriangulated graph, of which the treewidth is at most k we show there exists an O(n2) algorithm finding a path-decomposition with width at most 3k+4. If G[π] is a permutation graph with treewidth k, then we show that the pathwidth of G[π] is at most 2k, and we give an algorithm which constructs a path-decomposition with width at most 2k in time O(nk). We assume that the permutation π is given. In this paper we also discuss the problem of finding an approximation for the treewidth and pathwidth of cocomparability graphs. We show that, if the treewidth of a cocomparability graph is at most k, then the pathwidth is at most O(k 2), and we give a simple algorithm finding a path-decomposition with this width. The running time of the algorithm is dominated by a coloring algorithm of the graph. Such a coloring can be found in time O(n 3).

If the treewidth is bounded by some constant, previous results (i.e. [10, 21]), show that, once the approximations are given, the exact treewidth and pathwidth can be computed in linear time for all these graphs.

This author is supported by the foundation for Computer Science (S.I.O.N) of the Netherlands Organization for Scientific Research (N.W.O.).

This author is partially supported by by the ESPRIT Basic Research Actions of the EC under contract 7141 (project ALCOM II).

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Authors and Affiliations

  1. Department of Computer Science, Utrecht University, P.O.Box 80.089, 3508, TB Utrecht, The Netherlands

    Ton Kloks & Hans Bodlaender

Authors
  1. Ton Kloks
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  2. Hans Bodlaender
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Editor information

Toshihide Ibaraki Yasuyoshi Inagaki Kazuo Iwama Takao Nishizeki Masafumi Yamashita

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© 1992 Springer-Verlag Berlin Heidelberg

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Kloks, T., Bodlaender, H. (1992). Approximating treewidth and pathwidth of some classes of perfect graphs. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_64

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  • DOI: https://doi.org/10.1007/3-540-56279-6_64

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