New approximations for network reliability

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Networks Pub Date : 2024-03-04 DOI:10.1002/net.22215

Jason I. Brown, Theodore Kolokolnikov, Robert E. Kooij

引用次数: 0

Abstract

We introduce two new methods for approximating the all‐terminal reliability of undirected graphs. First, we introduce an edge removal process: remove edges at random, one at a time, until the graph becomes disconnected. We show that the expected number of edges thus removed is equal to , where is the number of edges in the graph, and is the average of the all‐terminal reliability polynomial. Based on this process, we propose a Monte‐Carlo algorithm to quickly estimate the graph reliability (whose exact computation is NP‐hard). Moreover, we show that the distribution of the edge removal process can be used to quickly approximate the reliability polynomial. We then propose increasingly accurate asymptotics for graph reliability based solely on degree distributions of the graph. These asymptotics are tested against several real‐world networks and are shown to be accurate for sufficiently dense graphs. While the approach starts to fail for “subway‐like” networks that contain many paths of vertices of degree two, different asymptotics are derived for such networks.

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网络可靠性的新近似值

我们介绍了两种近似无向图全端可靠性的新方法。首先，我们引入了一个边移除过程：随机移除边，每次移除一条，直到图变得断开。我们证明，这样移除的边的预期数量等于，其中，是图中的边的数量，是全端可靠性多项式的平均值。基于这一过程，我们提出了一种蒙特卡洛算法来快速估算图的可靠性（其精确计算是 NP 难的）。此外，我们还证明了边缘去除过程的分布可用于快速近似可靠性多项式。然后，我们仅根据图的度数分布，就提出了越来越精确的图可靠性渐近法。这些渐近线在几个真实世界的网络中进行了测试，结果表明，对于足够密集的图，这些渐近线是准确的。虽然这种方法在 "地铁状 "网络中开始失效，因为这种网络包含许多阶数为 2 的顶点路径，但我们也为这种网络推导出了不同的渐近线。

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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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.