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Embedding Classical Communication Topologies in the Scalable OPAM Architecture
September 1996 (vol. 7 no. 9)
pp. 979-992

Abstract—This paper presents novel embeddings of various classical topologies into the OPAM multicomputer. OPAM consists of a large number of processors that are connected by a two level, crossbar based interconnection network. The network combines a large, optical circuit-switched crossbar (reconfigurable network), with many small, packet-switching crossbars. The needed embedding is very different than the classical approaches. The goal in our case is to minimize routing decisions, so that communication requests can be satisfied by passing through two small crossbars. We show how to map parallel programs to this architecture using graph contraction notations. The family of parallel programs that we consider consists of multiple processes and communication links that are represented by connected, regular graphs such as rings, trees, two dimensional grids, cube connected cycles and hypercubes. In each case we show how to partition the vertex set of the program's graph to subsets, and how to assign each subset a cluster of processors in order to realize the topology of the given problem. In some of the cases we also prove that our partition and assignment algorithms are optimal.

[1] B. Bollobás, Extremal Graph Theory. London: Academic Press, 1978.
[2] S.N. Bhatt, F.R.K. Chung, F.T. Leighton, and A.L. Rosenberg, "Efficient Embeddings of Trees in Hypercubes," SIAM J. Computing, vol. 21, no. 1, pp. 151-162, 1992.
[3] C. Berge, Graphs and Hypergraphs, second edition. North-Holland, 1973.
[4] F. Berman and L. Snyder, "On Mapping Parallel Algorithms into Parallel Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 439-458, 1987.
[5] P.B. Berra, A. Ghafoor, M. Guizani, S.J. Marcinkowski, and P.A. Mitkas, "Optics and Supercomputing," Proc. IEEE, vol. 77, pp. 1,797-1,815, Dec. 1989.
[6] T.F. Chan and Y. Saad,“Multigrid algorithms on the hypercube multiprocessor,” IEEE Trans. Computers, pp. 969-977, Nov. 1986.
[7] M.Y. Chan, F. Chin, C.N. Chu, and W.K. Mak, "Dilation-5 Embedding of 3-Dimensional Grids into Hypercubes," Proc. Fifth Symp. Parallel and Distributed Processing, pp. 285-288, 1993.
[8] K. Efe,“Embedding mesh of trees in the hypercube,” J. Parallel and Distributed Computing, vol. 11, no. 3, pp. 222-230, Mar. 1991.
[9] D. Feitelson, L. Rudolph, and E. Schenfeld, "Limits on Free Space Optical Interconnection Networks," Optical Interconnections and Networks, Proc. SPIE, vol. 1,281, Mar. 1990.
[10] D. Feitelson, L. Rudolph, and E. Schenfeld, "An Optical Interconnection Network with 3D Layout and Distributed Control," Optical Interconnections and Networks, Proc. SPIE, vol. 1,281, Mar. 1990.
[11] D. Feitelson, L. Rudolph, and E. Schenfeld, "An Optical Free-Space Interconnection Network for Parallel Computers," Proc. 1990 Int'l Topical Meeting on Optical Computing—OC90,Kobe, Japan, Apr.8-12, 1990.
[12] L.S. Heath, A.L. Rosenberg, and B.T. Smith, "The Physical Mapping Problem for Parallel Architectures," J. ACM, vol. 35, no. 3, pp. 603-634, July 1988.
[13] C.-T. Ho and S.L. Johnsson, “Embedding Meshes in Boolean Cubes by Graph Decomposition,” J. Parallel and Distributed Computing, vol. 8, pp. 325-339, 1990.
[14] J.-W. Hong, K. Mehlhorn, and A.L. Rosenberg, "Cost Tradeoffs in Graph Embeddings," J. ACM, vol. 30, no. 4, pp. 709-728, 1983.
[15] I. Redmond and E. Schenfeld, "A Distributed, Reconfigurable Free-Space Optical Interconnection Network for Massively Parallel Processing Architectures," Proc. Optical Computing Conf. 1994—OC '94,Edinburgh, Aug. 1994.
[16] I. Redmond and E. Schenfeld, "Experimental Results of a 64 Channel, Free-Space Optical Interconnection Network for Massively Parallel Processing," Proc. Optical Computing Conf. 1994—OC '94,Edinburgh, Aug. 1994.
[17] L.H. Jamieson, "Characterizing Parallel Algorithms," The Chracteristics of Parallel Algorithms, pp. 65-100. MIT Press, 1987.
[18] S.L. Johnsson, "Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 133-172, 1987.
[19] A.R. Larrabee, K.E. Pennick, and S.M. Stern, "BBN Butterfly Parallel Processor," Programming Parallel Processors, pp. 43-57. Addison Wesley, 1988.
[20] Y.W. Ma and L. Tao, "Embeddings among Toruses and Meshes," Proc. Int'l Conf. Parallel Processing, pp. 178-187, 1987.
[21] E. Ma and L. Tao,“Embeddings among meshes and tori,” J. Parallel and Distributed Computing, vol. 18, pp. 44-55, 1993.
[22] R. Miller and Q.F. Stout, "Simulating Essential Pyramids," IEEE Trans. Computers, vol. 37, no. 12, pp. 1,642-1,648, Dec. 1988.
[23] F.P. Preparata and J. Vuillemin, “The Cube-Connected Cycles: A Versatile Network for Parallel Computation,” Comm ACM, vol. 24, no. 5, pp. 300-309, 1981.
[24] A. Rosenfeld, "Parallel Path Groups and Parallel Graph Contractions," The Book of L, pp. 369-382. Springer-Verlag, 1986.
[25] E. Schenfeld, "The Optical Parallel Architecture Mode (OPAM) Experiment - Project Plan and Motivations," Technical Report TR 88-17, Hebrew Univ. of Jerusalem, Dept. of Computer Science, Aug. 1988.
[26] E. Schenfeld, "A Parallel Architecture for a Digital Optical Computer," PhD thesis, Hebrew Univ. of Jerusalem, Dept. of Computer Science, 1990.
[27] C. L. Seitz,“The cosmic cube,”CACM, vol. 28, pp. 22–33, Jan. 1985.
[28] H.J. Siegel, W.G. Nation, C.P. Kruskal, and L.M. Napolitano, "Using the Multistage Cube Network Topology in Parallel Supercomputers," Proc. IEEE, vol. 77, no. 12, pp. 1,932-1,953, Dec. 1989.
[29] Q.F. Stout, "Hypercubes and Pyramids," Pyramidial Systems for Computer Vison.Berlin: Springer-Verlag, 1986.
[30] R. Varadarajan, "Embedding Shuffle Networks in Hypercubes," J. Parallel and Distributed Computing, vol. 11, no. 3, pp. 252-256, Mar. 1991.
[31] V. Gupta and E. Schenfeld, "Performance Analysis of a Synchronous, Circuit-Switched Interconnection Cached Network," Proc. Eighth ACM Int'l Conf. Supercomputing (ICS '94), pp. 246-255,Manchester, U.K., July, 1994.
[32] V. Gupta and E. Schenfeld, "NetSim—A Tool for Modeling the Performance of Circuit Switched Multicomputer Networks," Proc. Seventh Int'l Conf. Modeling Techniques and Tools for Computer Performance Evaluation,Vienna, Austria, May 1994. Lecture Notes in Computer Science 794, pp. 180-192, Springer-Verlag.
[33] V. Gupta and E. Schenfeld, "A Comparative Performance Study of an Interconnection Cached Network," Proc. 23rd Int'l Conf. Parallel Processing,St. Charles, Ill., Aug. 1994.
[34] A. Wagner, "Embedding All Binary Trees in the Hypercube," J. Parallel and Distributed Computing, vol. 18, pp. 33-43, 1993.
[35] A. Youssef and B. Narahari, "Banyan-Hypercube Networks," IEEE Trans. Parallel and Distributed Systems, vol. 1, no. 2, pp. 160-169, Apr. 1990.

Index Terms:
Graph contractions; graph embeddings; interconnection networks; mapping algorithms; parallel programs.
Citation:
Amnon Barak, Eugen Schenfeld, "Embedding Classical Communication Topologies in the Scalable OPAM Architecture," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 9, pp. 979-992, Sept. 1996, doi:10.1109/71.536941
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