On Multicast Algorithms for Heterogeneous Networks of Workstations

Abstract

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(n2k). 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.