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Node-to-set and set-to-set cluster fault tolerant routing in hypercubes

机译:超立方体中的节点到集合和集合到集合的容错路由

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We study node-to-set and set-to-set fault tolerant routing problems is n-dimensional hypercubes H_n. node-to-set routing problem is that given a node s and a set of nodes T={t_1,..., t_k}, finds k node-disjoint paths s→t_i, 1≤i≤k. Set-to-set routing problem is that Given two sets of nodes S={s_1,...,s_k}and T={t_1,...,t_k}, finds k node-disjoint paths, each Path connects a node of S and a node of T. From Menger's theorem, it is known that these two Problems in H_n can tolerate at most n-k arbitrary faulty nodes. In this paper, we prove that Both routing problems can tolerate n-k arbitrary subgraphs(called cluster)of diam- Eter 1.
机译:我们研究的节点到集合和集合到集合的容错路由问题是n维超立方体H_n。节点到集合的路由问题是,给定一个节点s和一组节点T = {t_1,...,t_k},找到k个节点不相交的路径s→t_i,1≤i≤k。设置到设置的路由问题是,给定两组节点S = {s_1,...,s_k}和T = {t_1,...,t_k},找到k个节点不相交的路径,每个Path连接一个节点从门格定理可知,H_n中的这两个问题最多可以容忍nk个任意故障节点。在本文中,我们证明这两个路由问题都可以容忍直径1的n-k个任意子图(称为簇)。

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