A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. This defines an equivalence relation where two digraphs are equivalent if one can be obtained from the other by a sequence of such operations. We show that given an adjacency-list representation of a digraph G, many fundamental graph algorithms can be carried out on any member G' of G's equivalence class in O(n+m) time, where m is the number of arcs in G, not the number of arcs in G' . This may have advantages when G' is much larger than G. We use this to generalize to digraphs a simple O(n + m log n) algorithm of McConnell and Spinrad for finding the modular decomposition of undirected graphs. A key step is finding the strongly-connected components of a digraph F in G's equivalence class, where F may have ~(m log n) arcs.

Source : oai:HAL:inria-00100846v1

Volume: Vol. 5

Published on: January 1, 2002

Submitted on: March 26, 2015

Keywords: algorithmes de graphes,modular decomposition,data structures,search strategies,structures de données,stratégies de recherche,décomposition modulaire,efficient graph algorithms,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS]

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