Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations

Abstract. Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization problems. Accordingly, there has been a drive towards a practical, linear-time algorithm for the problem. This paper posits such an algorithm; we present a linear-time modular decomposition algorithm that proceeds in four straightforward steps. This is achieved by intro-ducing the notion of factorizing permutations to an earlier recursive ap-proach. The only data structure used is an ordered list of trees, and each of the four steps amounts to simple traversals of these trees. Previous al-gorithms were either exceedingly complicated or resorted to impractical data-structures.