On Multicast Algorithms for Heterogeneous Networks of Workstations

Networks of workstations (NOWs) provide an economical platform for high performance parallel computing. Such networks may comprise a variety of different types of workstations and network devices. This paper addresses the problem of efficient multicast in a heterogeneous communication model. Although the problem of finding optimal multicast schedules is known to be NP-complete in this model, a greedy algorithm has been shown experimentally to find good solutions in practice. In this paper we show that the greedy algorithm finds provably near-optimal schedules in polynomial time and that optimal schedules can be found in polynomial time when the number of distinct types of workstations is bounded by a constant. Specifically, this paper presents three results. First, when there are n workstations of some constant k distinct types, the greedy algorithm is shown to find schedules that complete at most a constant additive term later than optimal. Second, an algorithm is given that finds optimal schedules in time O(n^2k). Finally, it is shown that for the general problem, the greedy algorithm finds solutions that complete the multicast in at most twice the optimal time.