Reliable broadcasting in hypercubes using safety levels

Abstract

We consider a distributed broadcasting algorithm for faulty hypercubes using incomplete spanning binomial trees. A faulty hypercube is a connected hypercube with faulty nodes. The incomplete spanning binomial tree proposed in this paper is a useful structure for implementing broadcasting in faulty hypercubes. It is defined as a subtree of a regular spanning binomial tree that connects all the nonfaulty nodes. The root node of such a tree is called an l-node. A method is proposed to locate a large subset of the l-node set using the concept of safety level. An optimal broadcast initiated from a safe node is proposed. When a nonfaulty source node is unsafe and there are at most n-1 faulty nodes in a faulty n-dimensional hypercube, the proposed broadcasting scheme requires at most n+1 steps. Possible extensions of the safety level concept to cover a larger subset of l-nodes are also presented.