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This paper defines and describes the properties of a multicast virtual topology, the M-array and a resource-efficient variation, the REM-array. It is shown how several collective operations can be implemented efficiently using these virtual topologies, while maintaining low complexity. Because the methods are applicable to any parallel computing environment that supports multicast communication in hardware, they provide a framework for collective communication libraries that are portable and yet take advantage of such low-level hardware functionality. In particular, the paper describes the practical issues of using these methods in wormhole-routed massively parallel computers (MPCs) and in workstation clusters connected by Asynchronous Transfer Mode (ATM) networks. Performance results are given for both environments.

Multicast Virtual Topologies for Collective Communication in MPCs and ATM Clusters