A survey of the algorithmic aspects of modular decomposition

Modular decomposition is a technique that applies to (but is not restricted to) graphs. The notion of a module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems. Since the first polynomial time algorithm in the early 1970’s, the algorithmic of the modular decomposition has known an important development. This paper survey the ideas and techniques that arose from this line of research.