A pratical and efficient algorithm for substitution decomposition

Elias Dahlhaus, Jens Gustedt, and Ross McConnell

appeared in SODA'97

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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.

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