• Publication
  • 1998
  • Issue No. 5 - May
  • Abstract - A Spanning Multichannel Linked Hypercube: A Gradually Scalable Optical Interconnection Network for Massively Parallel Computing
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Spanning Multichannel Linked Hypercube: A Gradually Scalable Optical Interconnection Network for Massively Parallel Computing
May 1998 (vol. 9 no. 5)
pp. 497-512

Abstract—A new, scalable interconnection topology called the Spanning Multichannel Linked Hypercube (SMLH) is proposed. This proposed network is very suitable to massively parallel systems and is highly amenable to optical implementation. The SMLH uses the hypercube topology as a basic building block and connects such building blocks using two-dimensional multichannel links (similar to spanning buses). In doing so, the SMLH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SMLH topology supports many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SMLH network is its ability to support a large number of processors with the possibility of maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. It is shown that the SMLH network provides better average message distance, average traffic density, and queuing delay than many similar networks, including the binary hypercube, the SBH, etc. Additionally, the SMLH has comparable performance to other high-performance hypercubic networks, including the Generalized Hypercube and the Hypermesh. An optical implementation methodology is proposed for SMLH. The implementation methodology combines both the advantages of free space optics with those of wavelength division multiplexing techniques. A detailed analysis of the feasibility of the proposed network is also presented.

[1] K. Hwang, Advanced Computer Architecture: Parallelism, Scalability, Programmability. McGraw-Hill, 1993.
[2] H.J. Siegel, Interconnection Networks for Large-Scale Parallel Processing, Second Ed., McGraw-Hill, New York, 1990.
[3] H.S. Stone and J. Cocke, "Computer Architecture in the 1990s," Computer, vol. 24, no. 9, pp. 30-38, Sept. 1991.
[4] A. Louri and H. Sung, "3D Optical Interconnects for High-Speed Interchip and Interboard Communications," Computer, vol. 27, no. 10, pp. 27-37, Oct. 1994.
[5] 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.
[6] S. Felperin, L. Gravano, G. Pifarre, and J. Sanz, "Fully-adaptive routing: Packet switching performance and wormhole algorithms," Proc. Supercomputing '91, pp. 654-663, 1991.
[7] J. Kim and C.R. Das, “Hypercube Communication Delay with Wormhole Routing,” IEEE Trans. Computers, vol. 43, no. 7, pp. 806-814, July 1994.
[8] Y. Saad and M. Schultz, "Topological Properties of Hypercubes," IEEE Trans. Computers, vol. 37, no. 7, pp. 867-872, July 1988.
[9] K. Ghose and K.R. Desai, "Hierarchical Cubic Networks," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 4, pp. 427-435, Apr. 1995.
[10] J.M. Kumar and L.M. Patnaik, "Extended Hypercube: A Hierarchical Interconnection Network of Hypercubes," IEEE Trans. Parallel and Distributed Systems, pp. 45-57, 1992.
[11] N.-F. Tzeng and S. Wei, “Enhanced Hypercubes,” IEEE Trans. Computers, vol. 40, no. 3, pp. 284-294, Mar. 1991.
[12] L.N. Bhuyan and D.P. Agrawal, "Generalized Hypercube and Hyperbus Structures Constructing Massively Parallel Computers," IEEE Trans. Computers, vol. 33, pp. 323-333, 1984.
[13] Q.M. Malluhi and M.A. Bayoumi, "The Hierarchical Hypercube: A New Interconnection Topology for Massively Parallel Systems," IEEE Trans. Parallel and Distributed Systems, vol. 5, no. 1, pp. 17-30, Jan. 1994.
[14] C. Chen, D.P. Agrawal, and J.R. Burke, "dBCube: A New Class of Hierarchical Multiprocessor Interconnection Networks with Area Efficient Layout," IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 1, pp. 1,332-1,344, Jan. 1993.
[15] K. Efe, “The Crossed Cube Architecture for Parallel Computing,” IEEE Trans. Parallel and Distributed Systems, vol. 3, no. 5, pp. 513-524, Sept.-Oct. 1992.
[16] J.R. Goodman and C.H. Sequin, "Hypertree: A Multiprocessor Interconnection Topology," IEEE Trans. Computers, vol. 30, pp. 923-933, 1981.
[17] A. Louri and H. Sung, "A Scalable Optical Hypercube-Based Interconnection Network for Massively Parallel Computing," Applied Optics, vol. 33, pp. 7,588-7,598, Nov. 1994.
[18] A. Louri and H. Sung, "An Optical Multi-Mesh Hypercube: A Scalable Optical Interconnection Network for Massively Parallel Computing," IEEE J. Lightwave Technology, vol. 12, pp. 704-716, Apr. 1994.
[19] A. Louri and S. Furlonge, "Feasibility Study of a Scalable Optical Interconnection Network for Massively Parallel Processing Systems," Applied Optics, vol. 35, pp. 1,296-1,308, Mar. 1996.
[20] A. Louri, S. Furlonge, and C. Neocleous, "Experimental Demonstration of the Optical Multi-Mesh Hypercube: A Scalable Interconnection Network for Multiprocessors and Multicomputers.," Applied Optics, vol. 35, no. 35, pp. 6,909-6,920, Dec. 1996.
[21] L.D. Wittie, "Communication Structures for Large Networks of Microcomputers," IEEE Trans. Computers, vol. 30, no. 4, pp. 264-273, Apr. 1981.
[22] G. Lerman and L. Rudolph, Parallel Evolution of Parallel Processors.New York: Plenum Press, 1993.
[23] M.R. Feldman, C.C. Guest, T.J. Drabik, and S.C. Esner, "Comparison Between Electrical and Free Space Optical Interconnects for Fine Grain Processor Arrays Based on Connection Density Capabilities," Applied Optics, vol. 28, pp. 3,820-3,829, 1989.
[24] J.W. Goodman, F.J. Leonberger, S.Y. Kung, and R.A. Athale, "Optical Interconnections for VLSI systems," Proc. IEEE, vol. 72, pp. 850-866, July 1984.
[25] D.M. Chiarulli, S.P. Levitan, R.G. Mehlen, M. Bidnurkar, R. Ditmore, G. Gravenstreter, Z. Guo, C. Qiao, M.F. Sakr, and J.P. Teza, "Optoelectronic Buses for High-Performance Computing," Proc. IEEE, vol. 82, no. 11, pp. 1,701-1,710, Nov. 1994.
[26] P.W. Dowd, "Wavelength Division Multiple Access Channel Hypercube Processor Interconnection," IEEE Trans. Computers, vol. 41, no. 10, pp. 1,223-1,241, Oct. 1992.
[27] Y. Li, A.W. Lohmann, and S.B. Rao, "Free-Space Optical Mesh-connected Bus Networks Using Wavelength-Division Multiple Access," Applied Optics, vol. 32, pp. 6,425-6,437, 1993.
[28] 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.
[29] D.S. Miller, "Optics for Low Energy Communication Inside Digital Processors: Quantum Detectors, Sources, and Modulators as Efficient Impedance Converters," Optics Letters, vol. 14, pp. 146-148, 1989.
[30] A.A. Sawchuk, C.S. Raghavandra, B.K. Jenkins, and A. Varma, “Optical Crossbar Networks,” IEEE Computer, vol. 20, no. 6, pp. 50–62, June 1987.
[31] D.P. Agrawl, C. Chen, and J.R. Burke, "A Comparison of Hybrid Graph Based Topologies," IEEE Computer Society Techinal Committee on Computer Architecture Newsletter, E.F. Gehringer, ed., pp. 5-8, Winter 1994-95.
[32] V. Kumar, A. Grama, A. Gupta, and G. Karypis, Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin Cummings, 1994.
[33] T. Szymanski, "Hypermeshes: Optical Interconnection Networks for Parallel Computing," J. Parallel and Distribted Computing, vol. 26, pp. 1-23, 1995.
[34] D. Reed and R. Fujimoto, Multicomputer Networks: Message-Based Parallel Processing. MIT Press, 1987.
[35] 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.
[36] E. Ganesan and D.K. Pradhan,“The hyper-de Bruijn multiprocessor networks: Scalable versatile architecture,” IEEE Trans. Parallel and Distributed Systems, vol. 4, no. 9, pp. 962-978, Sept. 1993.
[37] S.R. Öhring and S.K. Das, "The Folded Petersen Cube Network: New Competitors for the Hypercubes," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 2, pp. 151-168, Feb. 1996.
[38] L. Klienrock, Queueing Systems: Vol. II, Computer Applications.New York: Wiley, 1976.
[39] P. Sweazey, "Limits of Performance of Backplane Buses," Digital Bus Handbook.New York: McGraw-Hill, 1990.
[40] A.D. McAulay, Optical Computer Architectures: The Application of Optical Concepts to Next Generation Computers. John Wiley and Sons, 1991.
[41] A. Louri and H. Sung, "Efficient Implementation Methodology for Three-Dimensional Space-Invariant Hypercube-Based Free-Space Optical Interconnection Networks," Applied Optics, vol. 32, pp. 7,200-7,209, Dec. 1993.
[42] A. Cisneros and C.A. Brackett, "A Large ATM Switch Based on Memory Switches and Optical Star Couplers," IEEE J. Selected Areas Comm., vol. 9, pp. 1,348-1,360, Oct. 1991.
[43] P.F. Moulton, "Tunable Solid State Lasers," Proc. IEEE, vol. 80, pp. 348-364, Mar. 1992.
[44] B.D. Metcalf and J.F. Providakes, "High-Capacity Wavelength Demultiplexer with a Large-Diameter GRIN Rod Lens," Applied Optics, vol. 21, pp. 794-796, 1982.
[45] F.N Tinofeev, P. Bayvel, J.E. Midwinter, and M.N. Sokolskii, "High-Performance, Free-Space Ruled Concave Grating Demultiplexer," Electronics Letters, vol. 31, pp. 2,200-2,201, Dec. 1995.
[46] F.N Tinofeev, P. Bayvel, J.E. Midwinter, M.N. Sokolskii, E.G Churin, and A. Stavdas, "Free-Space Aberration-Corrected Grating Demultiplexer for Application in Densely-Spaced, Subnanometer Wavelength-Routed Optical Networks.," Electronics Letters, vol. 31, pp. 1,368-1,370, Aug. 1995.
[47] T.V. Moui, "Receiver Design for High-Speed Optical Fiber Systems," IEEE J. Lightwave Technology, pp. 243-267, 1984.
[48] D. Israel, R. Baets, M.J. Goodwin, N. Shaw, M.D. Salik, and C.J. Groves-Kirkby, "Comparison of Different Polymetric Multimode Star Couplers for Backplane Optical Interconnect," IEEE J. Lightwave Technology, vol. 13, pp. 1,057-1,064, June 1995.
[49] R.A. Morgan, "Advances in Vertical Cavity Surface Emitting Lasers," Proc. SPIE, vol. 2,147, pp. 97-119, 1994.
[50] A. Takai, T. Kato, S. Yamashita, S. Hanatani, Y. Motegi, K. Ito, H. Abe, and H. Kodera, "200-Mb/s/ch 100m Optical Subsystem Interconnections Using 8-channel 1.3 m Laser Diode Arrays and Single-Mode Fiber Arrays," IEEE J. Lightwave Technology, vol. 12, pp. 260-269, Feb 1994.
[51] N.K. Shankaranarayanan, U. Koren, B. Glance, and G. Wright, "Two-Section dBr Laser Transmitters with Accurate Channel Spacing and Fast Arbitrary-Sequence Tuning for FDMA Networks," Technical Digest of Fiber Optical Comm., pp. 36-37.Washington, DC: Optical Soc. of America, 1994.

Index Terms:
Interconnection networks, scalability, massively parallel processing, optical interconnects, wavelength division multiplexing, product networks.
Citation:
Ahmed Louri, Brent Weech, Costas Neocleous, "A Spanning Multichannel Linked Hypercube: A Gradually Scalable Optical Interconnection Network for Massively Parallel Computing," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 5, pp. 497-512, May 1998, doi:10.1109/71.679219
Usage of this product signifies your acceptance of the Terms of Use.