
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
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. 979992, September, 1996.  
BibTex  x  
@article{ 10.1109/71.536941, author = {Amnon Barak and Eugen Schenfeld}, title = {Embedding Classical Communication Topologies in the Scalable OPAM Architecture}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {7}, number = {9}, issn = {10459219}, year = {1996}, pages = {979992}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.536941}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  Embedding Classical Communication Topologies in the Scalable OPAM Architecture IS  9 SN  10459219 SP979 EP992 EPD  979992 A1  Amnon Barak, A1  Eugen Schenfeld, PY  1996 KW  Graph contractions; graph embeddings; interconnection networks; mapping algorithms; parallel programs. VL  7 JA  IEEE Transactions on Parallel and Distributed Systems ER   
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 circuitswitched crossbar (reconfigurable network), with many small, packetswitching 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. 151162, 1992.
[3] C. Berge, Graphs and Hypergraphs, second edition. NorthHolland, 1973.
[4] F. Berman and L. Snyder, "On Mapping Parallel Algorithms into Parallel Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 439458, 1987.
[5] P.B. Berra, A. Ghafoor, M. Guizani, S.J. Marcinkowski, and P.A. Mitkas, "Optics and Supercomputing," Proc. IEEE, vol. 77, pp. 1,7971,815, Dec. 1989.
[6] T.F. Chan and Y. Saad,“Multigrid algorithms on the hypercube multiprocessor,” IEEE Trans. Computers, pp. 969977, Nov. 1986.
[7] M.Y. Chan, F. Chin, C.N. Chu, and W.K. Mak, "Dilation5 Embedding of 3Dimensional Grids into Hypercubes," Proc. Fifth Symp. Parallel and Distributed Processing, pp. 285288, 1993.
[8] K. Efe,“Embedding mesh of trees in the hypercube,” J. Parallel and Distributed Computing, vol. 11, no. 3, pp. 222230, 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 FreeSpace Interconnection Network for Parallel Computers," Proc. 1990 Int'l Topical Meeting on Optical Computing—OC90,Kobe, Japan, Apr.812, 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. 603634, 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. 325339, 1990.
[14] J.W. Hong, K. Mehlhorn, and A.L. Rosenberg, "Cost Tradeoffs in Graph Embeddings," J. ACM, vol. 30, no. 4, pp. 709728, 1983.
[15] I. Redmond and E. Schenfeld, "A Distributed, Reconfigurable FreeSpace 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, FreeSpace 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. 65100. MIT Press, 1987.
[18] S.L. Johnsson, "Communication Efficient Basic Linear Algebra Computations on Hypercube Architectures," J. Parallel and Distributed Computing, vol. 4, pp. 133172, 1987.
[19] A.R. Larrabee, K.E. Pennick, and S.M. Stern, "BBN Butterfly Parallel Processor," Programming Parallel Processors, pp. 4357. Addison Wesley, 1988.
[20] Y.W. Ma and L. Tao, "Embeddings among Toruses and Meshes," Proc. Int'l Conf. Parallel Processing, pp. 178187, 1987.
[21] E. Ma and L. Tao,“Embeddings among meshes and tori,” J. Parallel and Distributed Computing, vol. 18, pp. 4455, 1993.
[22] R. Miller and Q.F. Stout, "Simulating Essential Pyramids," IEEE Trans. Computers, vol. 37, no. 12, pp. 1,6421,648, Dec. 1988.
[23] F.P. Preparata and J. Vuillemin, “The CubeConnected Cycles: A Versatile Network for Parallel Computation,” Comm ACM, vol. 24, no. 5, pp. 300309, 1981.
[24] A. Rosenfeld, "Parallel Path Groups and Parallel Graph Contractions," The Book of L, pp. 369382. SpringerVerlag, 1986.
[25] E. Schenfeld, "The Optical Parallel Architecture Mode (OPAM) Experiment  Project Plan and Motivations," Technical Report TR 8817, 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. 1,9321,953, Dec. 1989.
[29] Q.F. Stout, "Hypercubes and Pyramids," Pyramidial Systems for Computer Vison.Berlin: SpringerVerlag, 1986.
[30] R. Varadarajan, "Embedding Shuffle Networks in Hypercubes," J. Parallel and Distributed Computing, vol. 11, no. 3, pp. 252256, Mar. 1991.
[31] V. Gupta and E. Schenfeld, "Performance Analysis of a Synchronous, CircuitSwitched Interconnection Cached Network," Proc. Eighth ACM Int'l Conf. Supercomputing (ICS '94), pp. 246255,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. 180192, SpringerVerlag.
[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. 3343, 1993.
[35] A. Youssef and B. Narahari, "BanyanHypercube Networks," IEEE Trans. Parallel and Distributed Systems, vol. 1, no. 2, pp. 160169, Apr. 1990.