On-line Multicasting in Directed Graphs Work in progress

In this paper we study the problem of on-line multicasting on directed graphs, and we demonstrate the competitiveness of a greedy algorithm in a worst case analysis. We prove that the greedy algorithm performs almost as well as any on-line algorithm: the greedy upper bound is very close to the lower bound of any on-line algorithm. First, we improve on the upper bound of the oo-line greedy algorithm on undirected graphs with a simpler than the previous proof. Assume that A is the measure of asymmetry in a graph and M the size of the multicast group. For highly asymmetric graphs, we prove that the performance of the greedy algorithm is tightly bounded by (M), and prove that this is also the lower bound for any algorithm. For less asymmetric graphs, the greedy algorithm is bounded above by O(A log(M)). For these graphs, we prove that any algorithm performs at least as bad as O(A log(M)= log(A)).