多路径切割的区域生长
Region growing for multi-route cuts
摘要：
本文研究了若干多路割问题：给定图G =（V，E）和节点对的连通度阈值k_（u，v），目标是找到一个最小代价的边或顶点集，删除这些边或顶点使每对（u，v）之间的连通度严格地低于给定的阈值。这些问题出现在通信网络的可靠性背景下;它们是传统最小割问题的自然推广，其中阈值为1（我们希望完全分离对）或无穷大（我们不关心对的连通性）。我们提供了第一个非平凡的近似的问题，包括节点不相交和边缘不相交的连通性阈值的一些变种。我们的工作的一个主要贡献是一个扩展的区域增长技术近似最小多路设置。当连通性阈值为2或无穷大（“2-路由切割”的情况下），我们得到多项式近似，同时满足阈值。对于任意的连通性阈值，这种方法导致双准则近似，我们近似地满足阈值，并近似地最小化成本。我们提出了一些不同的算法，实现不同的成本连接权衡。
英文摘要：
We study a number of multi-route cut problems: given a graph G=(V,E) and connectivity thresholds k_(u,v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between every pair (u,v) to strictly below its given threshold. These problems arise in the context of reliability in communication networks; They are natural generalizations of traditional minimum cut problems where the thresholds are either 1 (we want to completely separate the pair) or infinity (we don't care about the connectivity for the pair). We provide the first non-trivial approximations to a number of variants of the problem including for both node-disjoint and edge-disjoint connectivity thresholds. A main contribution of our work is an extension of the region growing technique for approximating minimum multicuts to the multi-route setting. When the connectivity thresholds are either 2 or infinity (the "2-route cut" case), we obtain polylogarithmic approximations while satisfying the thresholds exactly. For arbitrary connectivity thresholds this approach leads to bicriteria approximations where we approximately satisfy the thresholds and approximately minimize the cost. We present a number of different algorithms achieving different cost-connectivity tradeoffs.
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