Abstract
In this paper, we study the problem of multicast routing on directed graphs. We define the asymmetry of a graph to be the maximum ratio of weights on opposite directed edges between a pair of nodes for all node-pairs. We examine three types of problems according the membership behavior: (i) the static, (ii) the join-only, (iii) the join-leave problems. We study the effect of the asymmetry on the worst case performance of two algorithms: the Greedy and Shortest Paths algorithms. The worst case performance of Shortest Paths is poor, but it is affected by neither the asymmetry nor the membership behavior. In contrast, the worst case performance of Greedy is a proportional to the asymmetry in a some cases. We prove an interesting result for the join-only problem: the Greedy algorithm has near-optimal on-line performance.
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