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

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 − k)!))-time (=O(k logn)) 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.