Future high-speed communication networks that use bandwidth reservation for quality-of-service guarantees depend greatly on multicast routing and admission control mechanisms. This paper presents a study of both the offline and the online versions of the multicast routing and admission control problem on unit-capacity graphs. The authors propose algorithms for tree and mesh topologies, since these form the basis of many existing communication networks. The objective function is to maximize the total number of accepted requests on the systems. The problem is a generalization of the edge-disjoint paths problem, and is NP-hard both on trees and meshes. They argue that in the multicast setting, polylogarithmic-competitive randomized algorithms are possible for restricted topologies, and they derive algorithms that accept multicasts that pass initial screening for routability with roughly equal probability. The authors also present a constant-factor approximation algorithm on trees and demonstrated how it gives a constant factor approximation of the optimal solution.

The paper is quite well written, with numerous descriptions of the various algorithms and proofs of theorems and lemmas that support the theorems. The paper could have been more readable if the descriptions of the algorithms had been augmented with diagrammatic illustrations.