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AnO(n 2) incremental algorithm for modular decomposition of graphs and 2-structures

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Abstract

This paper gives anO(n 2) incremental algorithm for computing the modular decomposition of 2-structures [1], [2]. A 2-structure is a type of edge-colored graph, and its modular decomposition is also known as the prime tree family. Modular decomposition of 2-structures arises in the study of relational systems. The modular decomposition of undirected graphs and digraphs is a special case, and has applications in a number of combinatorial optimization problems. This algorithm generalizes elements of a previousO(n 2) algorithm of Muller and Spinrad [3] for the decomposition of undirected graphs. However, Muller and Spinrad's algorithm employs a sophisticated data structure that impedes its generalization to digraphs and 2-structures, and limits its practical use. We replace this data structure with a scheme that labels each edge with at most one node, thereby obtaining an algorithm that is both practical and general to 2-structures.

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Author notes

  1. R. M. McConnell

    Present address: Department of Mathematics and Computer Science, Amherst College, 01002, Amherst, MA, USA

Authors and Affiliations

  1. Department of Computer Science, University of Colorado at Boulder, 80309-0430, Boulder, CO, USA

    R. M. McConnell

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  1. R. M. McConnell
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Communicated by K. Mehlhorn.

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McConnell, R.M. AnO(n 2) incremental algorithm for modular decomposition of graphs and 2-structures. Algorithmica 14, 229–248 (1995). https://doi.org/10.1007/BF01206330

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  • DOI: https://doi.org/10.1007/BF01206330

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