A Pratical and Efficient Algorithm for Substitution Decomposition

Abstract : We give a simple recursive algorithm for modular decomposition of undirected graphs that runs in O(n + m alpha(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.