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Efficient and practical modular decomposition

Dahlhaus, Elias; Gustedt, Jens; McConnell, Ross

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We give a simple recursive algorithm for modular decomposition of undirected graphs that runs in O(n + m α(m,n)) time. Previous algorithms with this bound are of theoretical use only. By adding some data structure tricks, we get a much simpler proof of an O(n+m) bound than was previously available. A key element of the algorithm is a procedure for finding a depth-first forest on the complement of a directed graph G in time proportional to the size of G.