The multicast admission control and routing problem can be defined as follows: network users issue online requests for connections to various multicast sources. The network either accepts a request or rejects it (the admission control decision). If the request is accepted, a path with sufficient bandwidth is established from the requesting user either to the source, or to one of the users previously connected to the same source (the routing decision). The goal of the admission control and routing algorithms is to maximize the total number of users connected, subject to the network capacity constraints. This problem can be reduced to the following online maximal dense tree problem: network users issue online requests to the single multicast source, and the problem again is that of admission control and routing. The objective, however, is to maximize the total number of connections while keeping the connection density, i.e. the ratio of accepted requests to the weight of the spanning tree, sufficiently high. Informally, the online maximal dense tree algorithm must “gamble” on certain geographic areas, connecting nodes which are unprofitable to start with, in the hope that eventually enough requests will arrive in the vicinity of its path to the root to make the investment profitable. This paper presents a randomized online algorithm for the maximal dense tree problem that guarantees to *Supported by NSF contract9114440-CCR, ARPA/Army contract DABT63-93-C-O038, ARPA/Air Force Contract F19628-95-C-0137, and NIST/USRA Contract 5555-47. Tripurari Singh Dept. of Computer Science Johns Hopkins University tsingh~cs.jhu.edu
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