Matrix Operations Using Arrays with Reconfigurable Optical Buses*

This paper examines the possibility of implementing matrix operations on an array with reconfigurable optical buses (AROB). The AROB combines some of the advantages and characteristics of reconfigurable meshes and meshes with optical pipelined buses. This model is extremely flexible, as demonstrated by its ability to efficiently simulate CREW PRAMs and reconfigurable networks. A number of applications arc investigated and it is shown that many matrix operations can be implemented efficiently, reducing the time complexity and/or the cost of existing algorithms which are given for other models of parallel computation.

[1]  Sergio Pissanetzky,et al.  Sparse Matrix Technology , 1984 .

[2]  Johnnie W. Baker,et al.  A Constant Time Sorting Algorithm for a Three Dimensional Reconfigurable Mesh and Reconfigurable Network , 1995, Parallel Process. Lett..

[3]  Rami G. Melhem,et al.  Pipelined Communications in Optically Interconnected Arrays , 1991, J. Parallel Distributed Comput..

[4]  Yosi Ben-Asher,et al.  Ranking on Reconfigurable Networks , 1991, Parallel Process. Lett..

[5]  Viktor K. Prasanna,et al.  An O(1) Time Optimal Algorithm for Multiplying Matrices on Reconfigurable Mesh , 1993, Inf. Process. Lett..

[6]  F. Leighton,et al.  Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes , 1991 .

[7]  Quentin F. Stout,et al.  Reconfigurable SIMD massively parallel computers , 1991 .

[8]  Giovanni Manzini Sparse Matrix Vector Multiplication on Distributed Architectures: Lower Bounds and Average Complexity Results , 1994, Inf. Process. Lett..

[9]  Hungwen Li,et al.  Reconfigurable Massively Parallel Computers , 1991 .

[10]  D M Chiarulli,et al.  Coincident pulse techniques for multiprocessor interconnection structures. , 1990, Applied optics.

[11]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[12]  Hartmut Schmeck,et al.  Sparse Matrix Multiplication on a Reconfigurable Mesh , 1995, Aust. Comput. J..

[13]  Yi Pan Order statistics on optically interconnected multiprocessor systems , 1994, First International Workshop on Massively Parallel Processing Using Optical Interconnections.

[14]  Z. Zlatev On Some Pivotal Strategies in Gaussian Elimination by Sparse Technique , 1980 .

[15]  Prabhakar Ragde,et al.  The Parallel Simplicity of Compaction and Chaining , 1990, J. Algorithms.

[16]  Rami G. Melhem,et al.  Using Coincident Optical Pulses for Parallel Memory Addressing , 1987, Computer.

[17]  Chunming Qiao On Designing Communication-Intensive Algorithms for a Spanning Optical Bus Based Array , 1995, Parallel Process. Lett..

[18]  David Peleg,et al.  The Power of Reconfiguration , 1991, J. Parallel Distributed Comput..

[19]  V P Heuring,et al.  Bit-serial architecture for optical computing. , 1992, Applied optics.

[20]  Zicheng Guo,et al.  Optically Interconnected Processor Arrays with Switching Capability , 1994, J. Parallel Distributed Comput..

[21]  Larry Rudolph,et al.  Techniques for Parallel Manipulation of Sparse Matrices , 1989, Theor. Comput. Sci..

[22]  Viktor K. Prasanna,et al.  A Fast Algorithm for Computing a Histogram on Reconfigurable Mesh , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Rami G. Melhem,et al.  Space Multiplexing of Waveguides in Optically Interconnected Multiprocessor Systems , 1989, Comput. J..

[24]  Rami G. Melhem,et al.  Time-Division Optical Communications in Multiprocessor Arrays , 1993, IEEE Trans. Computers.

[25]  Giovanni Manzini sparse Matrix Computations on the Hypercube and Related Networks , 1994, J. Parallel Distributed Comput..

[26]  Gen-Huey Chen,et al.  Constant Time Sorting on a Processor Array with a Reconfigurable Bus System , 1990, Inf. Process. Lett..