arXiv 0710.39012007-10cs.DM

一种基于LexBFS的递归线性时间模分解算法

A recursive linear time modular decomposition algorithm via LexBFS

Derek Corneil, Michel Habib, Christophe Paul, Marc Tedder

备注：: An EA of this work appeared in ICALP'08. The arXiv v2 contains an appendix with some sketches of proofs. To date, complete proofs can only be found in the PhD of M. Tedder and spread over several chapters. This is a self-contained version. To ease the understanding, the noveI presentation enlights the combinatorial objects involved in the algorithm, which still relies on the same ideas

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AI总结：

针对现有线性时间模分解算法复杂的问题，结合已有算法范式，提出一种基于切片分解和有根有序树序列的更简单线性时间模分解算法。

摘要：

图G的模是指在图外拥有相同邻接点集合的顶点集合。图的模构成所谓的分拆族，因此可以用一棵唯一的树MD(G)表示，称为模分解树。受模在众多算法图论问题中的核心作用驱动，高效计算MD(G)的问题自20世纪70年代初就被研究。迄今为止，最优算法都能在线性时间内运行，但都相当复杂。通过结合此前为该问题开发的算法范式，我们能够提出一种更简单的线性时间算法，它依赖非常简单的数据结构，即切片分解和有根有序树序列。

英文摘要：

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.

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