最小k边连通生成子图的分布逼近

Michal Dory
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引用次数: 14

摘要

在最小k边连通生成子图(k-ECSS)问题中,目标是找到能抵抗最多k-1个边失效的最小权值子图。这是网络设计中的一个核心问题,也是最小生成树(MST)问题的自然推广。尽管分布式计算社区已经对MST问题进行了广泛的研究,但对于k≥2,在分布式设置中已知的较少。本文给出了CONGEST模型中k-ECSS的快速随机分布近似算法。我们的第一个贡献是对于2-ECSS的Õ (D +√)-round O(logn)-近似,对于n个顶点和直径D的图,我们的算法的时间复杂度几乎很紧,几乎与MST问题的时间复杂度相匹配。对于较大的常数k,我们给出Õ (n) - O(logn) -近似。此外,在非加权3-ECSS的特殊情况下,我们展示了如何将时间复杂度提高到O(D log^3n)轮。我们的结果都显著提高了以前算法的时间复杂度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distributed Approximation of Minimum k-edge-connected Spanning Subgraphs
In the minimum k-edge-connected spanning subgraph (k-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to k-1 edge failures. This is a central problem in network design, and a natural generalization of the minimum spanning tree (MST) problem. While the MST problem has been studied extensively by the distributed computing community, for k ≥2 less is known in the distributed setting. In this paper, we present fast randomized distributed approximation algorithms for k-ECSS in the CONGEST model. Our first contribution is an Õ (D + √ )-round O(logn )-approximation for 2-ECSS, for a graph with n vertices and diameter D. The time complexity of our algorithm is almost tight and almost matches the time complexity of the MST problem. For larger constant values of k we give an Õ (n) -round O(logn ) -approximation. Additionally, in the special case of unweighted 3-ECSS we show how to improve the time complexity to O(D log^3n ) rounds. All our results significantly improve the time complexity of previous algorithms.
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