An online throughput-competitive algorithm for multicast routing and admission control

We present the first polylog-competitive online algorithm for the general multicast admission control and routing problem in the throughput model. The ratio of the number of requests accepted by the optimum offline algorithm to the expected number of requests accepted by our algorithm is O((logn + log logM)(logn + logM) logn), where M is the number of multicast groups and n is the number of nodes in the graph. We show that this is close to optimum by presenting an Ω(logn logM) lower bound on this ratio for any randomized online algorithm against an oblivious adversary, when M is much larger than the link capacities. Our lower bound applies even in the restricted case where the link capacities are much larger than bandwidth requested by a single ✩ A preliminary version of these results appeared in the 9th ACM–SIAM Symposium on Discrete Algorithms, 1998. * Corresponding author. E-mail addresses: [email protected] (A. Goel), [email protected] (M.R. Henzinger), [email protected] (S. Plotkin). 1 Research supported by an NSF Career award, an Alfred P. Sloan Fellowship, and by Serge Plotkin’s ARO and NSF Grants. 2 The author was at the Digital Systems Research Center, Digital Equipment Corporation when this research was done. 3 Research supported by ARO Grant DAAH04-95-1-0121, NSF Grants CCR9304971/CCR9307045, and by a Terman Fellowship. 0196-6774/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jalgor.2004.11.001 2 A. Goel et al. / Journal of Algorithms 55 (2005) 1–20 multicast. We also present a simple proof showing that it is impossible to be competitive against an adaptive online adversary. As in the previous online routing algorithms, our algorithm uses edge-costs when deciding on which is the best path to use. In contrast to the previous competitive algorithms in the throughput model, our cost is not a direct function of the edge load. The new cost definition allows us to decouple the effects of routing and admission decisions of different multicast groups.  2004 Elsevier Inc. All rights reserved.