Neighbourhood Broadcasting and Broadcasting on the (n, k)-Star Graph

Authors:
L. He;K. Qiu;Z. Z. Shen
Affiliations:
Department of Computer Science, Brock University, St. Catharines, Canada L2S 3A1;Department of Computer Science, Brock University, St. Catharines, Canada L2S 3A1;Dept. of Computer Science and Technology, Plymouth State University, Plymouth, U.S.A. NH 03264
Venue:
ICA3PP '08 Proceedings of the 8th international conference on Algorithms and Architectures for Parallel Processing
Year:
2008

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Abstract

The (n, k)-star graph is a generalization of the star graph. We first present an optimal neighbourhood broadcasting algorithm for the (n, k)-star, which is then used to develop an optimal broadcasting algorithm for it. Both algorithms are for the single-port model of the network. While our neighbourhood broadcasting is the first such algorithm designed for the network, our optimal O(log(n!/(n驴 k)!))-time (=O(klogn)) broadcasting algorithm improves previous algorithms with O(kn) running time. For the all-port model, we first identify a minimum dominating set for the (n, k)-star. We then use it to find an optimal broadcasting algorithm on the all-port model of the (n, k)-star. The running time of this algorithm matches those of previous ones but the algorithm is simpler by using a dominating set instead of spanning trees. In addition, the algorithm has no redundancy in that no node receives the same message more than once.