## An O(n²) Incremental Algorithm for Modular Decomposition of Graphs and 2-Structures (1995)

Venue: | ALGORITHMICA |

Citations: | 7 - 3 self |

### BibTeX

@MISC{McConnell95ano(n²),

author = {R.M. McConnell},

title = {An O(n²) Incremental Algorithm for Modular Decomposition of Graphs and 2-Structures},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper gives an O(n²) incremental algorithm for computing the modular decomposition of 2-structure [1, 2]. A 2-structure is a type of edge-colored graph, and its modular decomposition is also known as the prime tree family. Modular decomposition of 2-structures arises in the study of relational systems. The modular decomposition of undirected graphs and digraphs is a special case, and has applications in a number of combinatorial optimization problems. This algorithm generalizes elements of a previous O(n²) algorithm of Muller and Spinrad [3] for the decomposition of undirected graphs. However, Muller and Spinrad's algorithm employs a sophisticated data structure that impedes its generalization to digraphs and 2-structures, and limits its practical use. We replace this data structure with a scheme that labels each edge with at most one node, thereby obtaining an algorithm that is both practical and general to 2-structures.