Linear-time modular decomposition of directed graphs

Abstract

Modular decomposition of graphs is a powerful tool with many applications in graph theory and optimization. There are efficient linear-time algorithms that compute the decomposition for undirected graphs. The best previously published time bound for directed graphs is O(n + m log n), where n is the number of vertices and m is the number of edges. We give an O(n + w)-time algorithm. © 2004 Elsevier B.V. All rights reserved.