A Study of Group-Tree Matching in Large Scale Group Communications

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 grouptree matching problem. We first formally define the problem, and formulate two versions of the problem: static and dynamic. Since the static version is the fundamental part of the problem, in this paper, we focus our efforts on this aspect. We analyze the static version problem and prove that it is NP-complete. To tackle this hard problem, we propose three algorithms: one optimal (using Integer Linear Programming, or ILP), one near-optimal (using Greedy method), and one pseudo-dynamic algorithm. Simulation studies are conducted to compare these three algorithms. Our results show that Greedy algorithm is a feasible solution and its performance is very close to the ILP optimal solution, while pseudo-dynamic algorithm is a good heuristic for many cases where Greedy does not work well. The study of group-tree matching in this paper not only provides solutions for the static version problem, but also paves the way for formally investigating the dynamic version problem.