一般模分解理论的数学性质
Algorithmic Aspects of a General Modular Decomposition Theory
摘要：
从模图分解的思想出发，提出了一种新的通用分解理论。这有助于统一不同结构的模块分解，包括（但不限于）图。此外，即使在图的情况下，术语“模块”不仅涵盖了经典的图模块，而且还允许处理2-连通组件，星形割集和其他顶点子集。主要的结果是，大多数好的算法工具开发的模块化分解的图仍然有效地适用于我们的一般化模块。此外，当一个本质公理被满足时，几乎所有的重要性质都可以被恢复。对于这种情况下，一个算法给出的Escherifeucht，Gabow，McConnell和Sullivan 1994年推广，并产生一个非常有效的解决方案，相关的分解问题。
英文摘要：
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs, the terminology ``module'' not only captures the classical graph modules but also allows to handle 2-connected components, star-cutsets, and other vertex subsets. The main result is that most of the nice algorithmic tools developed for modular decomposition of graphs still apply efficiently on our generalisation of modules. Besides, when an essential axiom is satisfied, almost all the important properties can be retrieved. For this case, an algorithm given by Ehrenfeucht, Gabow, McConnell and Sullivan 1994 is generalised and yields a very efficient solution to the associated decomposition problem.
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