Hierarchical Reliable Multicast: Performance Analysis and Optimal Placement of Proxies

This paper studies the use of multicast together with proxy nodes for reliably disseminating data from a single source to a large number of receivers. In order to achieve reliability, data must be retransmitted in case of loss either by the source or by special network nodes, called proxies. Each proxy is responsible for reliably delivering the data to a subgroup it is assigned. The multicast tree is partitioned into subgroups that form a hierarchy rooted at the source, hence the term hierarchical reliable multicast. The performance of this approach strongly depends on the topology and the loss characteristics of the underlying tree and the location of proxies. In the first part of the paper, we study the processing and bandwidth performance of such a reliable multicast dissemination given the tree and the placement of proxies. In the second part of the paper, we develop dynamic programming algorithms that give a placement of a fixed number of proxies on an arbitrary tree that minimizes the bandwidth used for reliable transfer. The first algorithm provides an optimal solution to the multicast proxies location problem in polynomial time, in the number of nodes and proxies. The second is an approximation algorithm that gives a solution with cost within a chosen precision from the optimal, in an improved running time. An optimal and an approximate solution are also provided for the proxies location problem if unicast is used for transmissions. Applications of this dynamic programming approach to related problems are discussed. q 2003 Elsevier B.V. All rights reserved.