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Safety Levels-An Efficient Mechanism for Achieving Reliable Broadcasting in Hypercubes
May 1995 (vol. 44 no. 5)
pp. 702-706

Abstract—We consider a distributed broadcasting algorithm for injured hypercubes using incomplete spanning binomial trees. An injured 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 injured hypercubes. It is defined as a subtree of a regular spanning binomial tree that connects all the nonfaulty nodes. We show that in an injured n-dimensional hypercube with m faulty nodes, there are at least 2n− 2m source nodes (called l-nodes), each of which can generate an incomplete spanning binomial tree. A method is proposed to locate a large subset of the l-node set using the concept of safety level. The safety level of each node in an n-dimensional hypercube can be easily calculated through n− 1 rounds of information exchange among neighboring nodes. 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 an injured n-dimensional hypercube, the proposed broadcasting scheme requires at most n+ 1 steps.

Index Terms:
Binomial trees, broadcasting, fault tolerance, hypercubes.
"Safety Levels-An Efficient Mechanism for Achieving Reliable Broadcasting in Hypercubes," IEEE Transactions on Computers, vol. 44, no. 5, pp. 702-706, May 1995, doi:10.1109/TC.1995.10003
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