Algorithms for the minimal cutsets enumeration of networks by graph search and branch addition

Heejong Suh, Carl K. Chang
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引用次数: 16

Abstract

This paper presents effective algorithms for enumerating the minimal cutsets of networks. After a graph is modeled after a network, first, by a graph method the spanning tree of the graph and binary tree whose event is complement to it are evaluated. The sub-vertex set represented by the binary tree is referenced, and an algorithm which evaluates the minimal cutsets is proposed. This algorithm requires a space memorizing a topology of the graph, and has a time complexity which is proportional to a number of the edges of the graph and the binary tree. Second, by adding the branch, an algorithm enumerating the cutsets, which separates the sub-vertex set and a disjoint vertex set of the graph, is proposed. This algorithm does not enumerate all the events which the vertex and edge set can have, and executes computation to only the number of minimal cutsets. The space needed is proportional to the square of the number of the vertexes, and time complexity is in the order of the number of cutsets. The reliability is computed from the events of cutset.
基于图搜索和分支加法的网络最小割集枚举算法
本文提出了一种有效的网络最小割集枚举算法。在对网络进行图的建模后,首先用图的方法求出图的生成树和与其互为补的二叉树。引用二叉树表示的子顶点集,提出了一种求最小割集的算法。该算法需要一个空间来存储图的拓扑结构,并且其时间复杂度与图和二叉树的边数成正比。其次,通过添加分支,提出了一种将图的子顶点集与不相交顶点集分离的割集枚举算法;该算法不列举顶点集和边集可能具有的所有事件,只对最小割集的个数进行计算。所需的空间与顶点数量的平方成正比,时间复杂度与切集数量的顺序成正比。可靠性是根据割集的事件来计算的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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