Worst case analysis of a greedy multicast algorithm in k-ary n-cubes

In this paper, we consider the problem of multicasting a message in k-ary n-cubes under the store-and-forward model. The objective of the problem is to minimize the size of the resultant multicast tree by keeping the distance to each destination over the tree the same as the distance in the original graph. In the following, we first propose an algorithm that grows a multicast tree in a greedy manner, in the sense that for each intermediate vertex of the tree, the outgoing edges of the vertex are selected in a non-increasing order of the number of destinations that can use the edge in a shortest path to the destination. We then evaluate the goodness of the algorithm in terms of the worst case ratio of the size of the generated tree to the size of an optimal tree. It is proved that for any k≥5 and n≥6, the performance ratio of the greedy algorithm is c×kn-o(n) for some constant 1/1.2≤c≤1/2.