A new approach to the design of collective communication operations in wormhole-routed mesh networks is described. The approach extends the concept of dominating sets in graph theory by accounting for the relative distance-insensitivity of the wormhole switching strategy and by taking advantage of a multiport communication architecture, which allows each node to simultaneously transmit messages on different outgoing channels. Collective communication operations are defined in terms of sets of extended dominating nodes (EDNs). The nodes in a set of EDNs can deliver (receive) messages to (from) a different, larger set of nodes in a single message-passing step under dimension-ordered wormhole routing and without channel contention among messages. The EDN model can be applied to different collective operations in 2D and 3D mesh networks. The authors focus on EDN-based broadcast and global combine operations. Performance evaluation results are presented that confirm the advantage of this approach over other methods.
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