As a mechanism to support group communications, multicasting faces a serious state scalability problem when there are large numbers of groups in the network: lots of resources (e.g., memory to maintain group state information) and control overhead (e.g., multicast tree setup and maintenance) are required to manage the groups. Recently, an efficient solution called aggregated multicast is proposed [8]. In this approach, groups are assigned to proper trees and multiple groups can share one delivery tree. A key problem in aggregated multicast is group-tree matching (i.e., matching groups to trees). In this paper, we investigate this group-tree matching problem. We first formally define the problem, and formulate two versions of the problem: static and dynamic. We analyze the static version of the problem and prove that it is NP-complete. To tackle this hard problem, we propose three algorithms: one optimal (using Linear Integer Programming, or ILP), one near-optimal (using Greedy method), and one pseudo-dynamic algorithm. For the dynamic version, we present a general heuristic on-line grouptree matching algorithm. Simulation studies are conducted to compare the three algorithms for the static version. Our results show that Greedy algorithm is a feasible solution to the static problem and its performance is very close the ILP optimal solution, while pseudo-dynamic algorithm is a good heuristic for many cases where Greedy does not work well. We also evaluate the performance of the heuristic online algorithm, and show that it is a practical solution to the dynamic on-line group-tree matching problem
