Linear-time modular decomposition of directed graphs
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+mlogn) O ( n + m log n ) , where n is the number of vertices and m  is the number of edges. We give an O(n+m) O ( n + m ) -time algorithm.
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