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All-to-All Personalized Communication in a Wormhole-Routed Torus
May 1996 (vol. 7 no. 5)
pp. 498-505

Abstract—All-to-all personalized communication, or complete exchange, is at the heart of numerous applications in parallel computing. It is one of the most dense communication patterns. In this paper, we consider this problem in a torus of any dimension with the wormhole-routing capability. We propose complete exchange algorithms that use optimal numbers of phases (if each side of the tori is a multiple of eight) or asymptotically optimal numbers of phases (otherwise). Interestingly, in order to achieve this, we only make weak assumptions—that a node is capable of sending and receiving at most one message at a time, and the network is capable of supporting the dimension-ordered (or e-cube) minimum routing.

[1] P. Berman, L. Gravano, J. Sanz, and G. Pifarre, "Adaptive Deadlock- and Livelock-Free Routing with All Minimal Paths in Torus Networks," Proc. Fourth ACM Symp. Parallel Algorithms and Architectures, June 1992.
[2] S.H. Bokhari, H. Berryman, "Complete Exchange on a Circuit Switched Mesh," Proc. Scalable High Performance Computing Conf., pp. 300-306, 1992.
[3] M.C. Co, "MP-1 Family Data-Parallel Computers," technical report.
[4] R. Cypher and L. Gravano, "Adaptive, Deadlock-Free Packet Routing in Torus Networks with Minimal Storage," Proc. Int'l Conf. Parallel Processing, pp. III-204-211, 1992.
[5] W.J. Dally and C.L. Seitz, "The Torus Routing Chip," J. Parallel and Distributed Computing, vol. 1, no. 3, pp. 187-196, 1986.
[6] W.J. Dally et al., "The J-Machine: A Fine-Grain Concurrent Computer," Proc. Information Processing 89, IFIP, pp. 1,147-1,153, 1989.
[7] S. Gupta, S. Hawkinson, and B. Baxter, "A Binary Interleaved Algorithm for Complete Exchange on a Mesh Architecture," technical report, Intel Corporation, 1994.
[8] H. Li and M. Maresca,“Polymorphic-torus network,” IEEE Trans. on Computers, vol. 38, no. 9, pp. 1345-1351, Sept. 1989.
[9] M. Maresca and H. Li,“Connection autonomy in SIMD computers: a VLSI implementation,”J. Parallel Distribut. Comput., vol. 7, pp. 302–320, 1989.
[10] L.M. Ni and P.K. McKinley, "A Survey of Wormhole Routing Techniques in Direct Networks," Computer, vol. 26, no. 2, pp. 62-76, Feb. 1993.
[11] D.S. Scott, "Efficient All-to-All Communication Patterns in Hypercube and Mesh Topologies," Proc. Sixth Conf. Distributed Memory Concurrent Computers, pp. 398-403, 1991.
[12] S.R. Seidel, "Circuit Switched vs. Store-and-Forward Solutions to Symmetric Communication Problems," Proc. Fourth Conf. Hypercube Concurrent Computers and Applications, pp. 253-255, 1989.
[13] N.S. Sundar, D.N. Jayasimha, D.K. Panda, and P. Sadayappan, "Complete Exchange in 2D Meshes," Proc. Scalable High Performance Computing Conf., pp. 406-413, 1994.
[14] M.R. Thistle and B.J. Smith, "A Processor Architecture for Horizon," Proc. Supercomputing, pp. 35-41, 1988.

Index Terms:
All-to-all personalized communication, complete exchange, collective communication, multicomputer network, parallel computing, torus, wormhole routing.
Yu-Chee Tseng, Sandeep K.S. Gupta, "All-to-All Personalized Communication in a Wormhole-Routed Torus," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 5, pp. 498-505, May 1996, doi:10.1109/71.503775
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