In this paper, we disprove the common assumption that the time for broadcasting in a mesh is at best proportional to the square root of the number of processors, at least in the presence of worm-hole routing. We present an optimal algorithm for broadcasting in mesh-connected distributed-memory architectures with worm-hole routing. By organizing the processing nodes in a logical spanning tree, the algorithm executes in time proportional to the logarithm of the number of nodes without inducing contention in the communication network. We restrict the number of nodes in each dimension of the processor mesh to be a power of two. Our method provides insight into how to avoid and/or reduce network contention on meshes for other communication operations. Experimental results on the Intel Touchstone Delta system are included.
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- Hoefler T and Moor D (2014). Energy, Memory, and Runtime Tradeoffs for Implementing Collective Communication Operations, Supercomputing Frontiers and Innovations: an International Journal, 1:2, (58-75), Online publication date: 9-Jul-2014.
Sack P and Gropp W Faster topology-aware collective algorithms through non-minimal communication Proceedings of the 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming, (45-54)- Sack P and Gropp W (2012). Faster topology-aware collective algorithms through non-minimal communication, ACM SIGPLAN Notices, 47:8, (45-54), Online publication date: 11-Sep-2012.
- Chan E, van de Geijn R, Gropp W and Thakur R Collective communication on architectures that support simultaneous communication over multiple links Proceedings of the eleventh ACM SIGPLAN symposium on Principles and practice of parallel programming, (2-11)
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- Tsai Y and McKinley P A dominating set model for broadcast in all-port wormhole-routed 2D mesh networks Proceedings of the 8th international conference on Supercomputing, (126-135)
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