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A new linear algorithm for Modular Decomposition

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Trees in Algebra and Programming — CAAP'94 (CAAP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 787))

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Abstract

We present here a new algorithm linear in time and space complexity for Modular Decomposition. This algorithm relies on structural properties of prime graphs (see theorems 7, and 8), on properties of modules (see property 1 and corollary 1) but also on the cograph recognition algorithm [CPS85]. Our algorithm builds and explores the decomposition tree of any undirected graph in a depth-first search way. As a by-product we show that a vertex-splitting operation is really a central tool for modular decomposition algorithms.

The authors wish to thank Bruno Courcelle, Hervé Dicky, Dieter Kratsch, Rolf Möhring, Stephan Olariu, Jerry Spinrad, Ross McConnel, and many others for stimulating and fruitful discussions on graph decompositions.

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Authors and Affiliations

  1. LIRMM, 161, Rue Ada, 34392, Montpellier cedex 5, France

    Alain Cournier & Michel Habib

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  1. Alain Cournier
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  2. Michel Habib
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Sophie Tison

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© 1994 Springer-Verlag Berlin Heidelberg

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Cournier, A., Habib, M. (1994). A new linear algorithm for Modular Decomposition. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017474

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  • DOI: https://doi.org/10.1007/BFb0017474

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  • Print ISBN: 978-3-540-57879-6

  • Online ISBN: 978-3-540-48373-1

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