A recursive linear time modular decomposition algorithm via LexBFS

TL;DR

This paper introduces a simpler, recursive linear-time algorithm for computing the modular decomposition tree of a graph, leveraging basic data structures to improve efficiency and simplicity over previous methods.

Contribution

It presents a novel, simpler linear-time algorithm for modular decomposition using slice decomposition and rooted ordered trees, improving on prior complex algorithms.

Findings

Algorithm runs in linear time

Uses simple data structures for implementation

Simplifies the process of modular decomposition

Abstract

A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree. Motivated by the central role of modules in numerous algorithmic graph theory questions, the problem of efficiently computing MD(G) has been investigated since the early 70's. To date the best algorithms run in linear time but are all rather complicated. By combining previous algorithmic paradigms developed for the problem, we are able to present a simpler linear-time that relies on very simple data-structures, namely slice decomposition and sequences of rooted ordered trees.