An algorithm for modular decomposition based on multiplexes

Abstract

Modular decomposition is instrumental in the the design of algorithms for solving many important graph theory problems. It has been applied towards developing recognition algorithms for many important perfect graph families. It also forms the basis of a number of efficient algorithms for solving combinatorial optimization problems on graphs.There are a number of efficient algorithms proposed in literature for computing the modular decomposition. Here we explore an O(n3) modular decomposition algorithm based on the theory of transitive orientation. The algorithm highlights how the problem of finding a transitive orientation is intimately related to that of finding the modular decomposition.