Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations

Authors:
Marc Tedder;Derek Corneil;Michel Habib;Christophe Paul
Affiliations:
Department of Computer Science, University of Toronto, ;Department of Computer Science, University of Toronto, ;LIAFA and the University of Paris 7 - Denis Diderot, ;CNRS - LIRMM, Univ. Montpellier II France (part of this research was conducted while on sabbatical in the School of Computer Science at the University of McGill),
Venue:
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Year:
2008

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Abstract

Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization problems. Accordingly, there has been a drive towards a practical, linear-time algorithm for the problem. This paper posits such an algorithm; we present a linear-time modular decomposition algorithm that proceeds in four straightforward steps. This is achieved by introducing the notion of factorizing permutations to an earlier recursive approach. The only data structure used is an ordered list of trees, and each of the four steps amounts to simple traversals of these trees. Previous algorithms were either exceedingly complicated or resorted to impractical data-structures.