A broadcasting algorithm on the arrangement graph
In this paper, we propose a distributed algorithm for one-to-all broadcasting on the arrangement graph. The algorithm exploits the rich topological properties of the (n, k)-arrangement graph to constitute the broadcasting binary tree and works recursively. When faulty links are encountered, the concepts of node-disjoint paths and virtual paths are used to deal with the broadcasting procedure. It is shown that the message can be broadcast to all n!/(n−k)! processors in O(k lg n) steps for fault-free mode, and in O(k(k+lg n)) for less than k(n−k)−1 faulty links.
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