Efficient and Scalable Routing Algorithms for Collective Communication Operations on 2D All-Port Torus Networks

Collective Communication Algorithms for 2D torus networks have been investigated quite extensively in the literature and two broad approaches, namely direct methods and indirect (message combining) methods are recognized in the field. While direct methods minimize the volume of data, the indirect methods reduce the number of message start-ups. Consequently, either a suite of algorithms must be employed for efficiency over a wide range of message lengths and communication operations or algorithms should be able to adapt themselves to the current case, possibly by switching between direct and indirect routing modes as appropriate. In this paper, we propose adaptive routing algorithms for all-port, wormhole routed, synchronous, 2D torus networks optimized for one-to-all broadcast,  gossiping and complete exchange collective communication operations. The proposed algorithms employ completely-connected subnetworks where complete exchange amongst the nodes in the subnetwork can be accomplished in one step only. Combined with suitable 2D plane tiling techniques, the proposed algorithms share the same set of primitive operations and yield superior performance compared to previously proposed methods, either pure or hybridized.