容错近似最短路径树
Fault-Tolerant Approximate Shortest-Path Trees
摘要：
网络的弹性是指当任何节点或链路发生故障时，网络仍能保持\emph{effectively}正常工作的能力。然而，为了降低运营和设置成本，网络的规模应该很小，这与弹性的要求相冲突。在本文中，我们针对{ \em广播}路由方案的突出情况解决了这种权衡，并且我们构建了有效的（即，稀疏和快速）\emph{fault-tolerant approximate shortest-path trees}，用于边和顶点\emph{single-failure}情况。特别是，对于一个$n$ -顶点非负加权图，并为任何常数$\varepsilon >0$，我们设计了两个结构的大小$O(\frac{n \log n}{\varepsilon^2})$，保证$(1+\varepsilon)$ -拉伸路径从选定的源也存在的边缘/顶点故障。这与目前最知名的解决方案相比具有优势，这些解决方案适用于尺寸为$O(n)$且拉伸因子为3的边缘失效情况，以及尺寸为$O(n \log n)$且拉伸因子为3的顶点失效情况。此外，我们还专注于未加权的情况下，我们证明了一个普通的$(α,β)$ -可略有增加，以建立有效的容错近似\emph{breadth-first-search trees}。
英文摘要：
The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the requirement of being resilient. In this paper we address this trade-off for the prominent case of the {\em broadcasting} routing scheme, and we build efficient (i.e., sparse and fast) \emph{fault-tolerant approximate shortest-path trees}, for both the edge and vertex \emph{single-failure} case. In particular, for an $n$-vertex non-negatively weighted graph, and for any constant $\varepsilon >0$, we design two structures of size $O(\frac{n \log n}{\varepsilon^2})$ which guarantee $(1+\varepsilon)$-stretched paths from the selected source also in the presence of an edge/vertex failure. This favorably compares with the currently best known solutions, which are for the edge-failure case of size $O(n)$ and stretch factor 3, and for the vertex-failure case of size $O(n \log n)$ and stretch factor 3. Moreover, we also focus on the unweighted case, and we prove that an ordinary $(α,β)$-spanner can be slightly augmented in order to build efficient fault-tolerant approximate \emph{breadth-first-search trees}.
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