A simple linear-time modular decomposition algorithm for graphs, using order extension

Abstract

The first polynomial time algorithm (script O sign(n4)) for modular decomposition appeared in 1972 [8] and since then there have been incremental improvements, eventually resulting in linear-time algorithms [22, 7,23,9]. Although having optimal time complexity these algorithms are quite complicated and difficult to implement. In this paper we present an easily implementable linear-time algorithm for modular decomposition. This algorithm uses the notion of factorizing permutation and a new data-structure, the Ordered Chain Partitions. © Springer-Verlag Berlin Heidelberg 2004.