Scheduling multicasts on unit-capacity trees and meshes

This paper studies the multicast routing and admission control problem on unit-capacity tree and mesh topologies in the throughput-model. The problem is a generalization of the edge-disjoint paths problem and is NPhard both on trees and meshes. We study both the offline and the online version of the problem: In the offline setting, we give the first constant-factor approximation algorithm for trees, and an O((log log n)*)-factor approximation algorithm for meshes, where n is the number of nodes in the graph. In the online setting, we give the first polylogarithrnic competitive online algorithm for tree and mesh topologies. No polylogarithmic-competitive algorithm is possible on general network topologies [8] and there exists a polylogarithmic lower bound on the competitive ratio of any online algorithm on tree topologies [l]. We prove the same lower bound for meshes.