连通顶点覆盖和团分解问题的自稳定算法
Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems
摘要：
在许多无线网络中，既没有固定的物理主干，也没有集中的网络管理。这种网络的节点必须自组织，以维持用于路由消息的虚拟骨干。此外，网络的任何节点都可以是恶意攻击的先验来源。因此，一方面主干网必须是容错的，另一方面它可以是有用的，以监测所有的网络通信，以确定攻击尽快。我们感兴趣的最小\emph{Connected Vertex Cover}问题，一个推广的经典最小顶点覆盖问题，它允许获得一个连接的骨干。最近，Delbot等人~ \cite{DelbotLP13}提出了一种新的集中式算法，具有恒定的近似比$2$。在本文中，我们提出了一个分布式和自稳定版本的算法具有相同的近似保证。据作者所知，这是第一个分布式和容错算法，这个问题。所考虑的问题的解决方法是基于一个连接的最小团分区的建设。因此，我们还设计了第一个分布式自稳定算法，这是独立的利益。
英文摘要：
In many wireless networks, there is no fixed physical backbone nor centralized network management. The nodes of such a network have to self-organize in order to maintain a virtual backbone used to route messages. Moreover, any node of the network can be a priori at the origin of a malicious attack. Thus, in one hand the backbone must be fault-tolerant and in other hand it can be useful to monitor all network communications to identify an attack as soon as possible. We are interested in the minimum \emph{Connected Vertex Cover} problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant approximation ratio of $2$ for this problem. In this paper, we propose a distributed and self-stabilizing version of their algorithm with the same approximation guarantee. To the best knowledge of the authors, it is the first distributed and fault-tolerant algorithm for this problem. The approach followed to solve the considered problem is based on the construction of a connected minimal clique partition. Therefore, we also design the first distributed self-stabilizing algorithm for this problem, which is of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
