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Abstract: We use an algebraic theory based on tensor products to model multistage interconnection networks. This algebraic theory has been used for designing and implementing block recursive numerical algorithms on shared-memory vector multiprocessors. In this paper, we focus on the modeling of multistage interconnection networks. The tensor product representations of the baseline network, the reverse baseline network, the indirect binary n-cube network, the generalized cube network, the omega network,... (Update)
Context of citations to this paper: More
.... in a wide spectrum of supercomputer architectures, as well as, the underlying hardware structures, like the interconnection networks [19, 20]. This, coupled with the availability of a methodology for translating algorithms expressed using the tensor product and other matrix...
.... output) Their properties have been studied with numerous mathematical approach (permutations, group or number theory) An algebraic theory [10] based on tensor products is presented, in order to specify and verify the properties of these networks. The skewing scheme we...
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BibTeX entry: (Update)
S. D. Kaushik, S. Sharma, and C.-H. Huang. An algebraic theory for modeling multistage interconnection networks. Journal of Information Science and Engineering, 9:1--26, 1993. http://citeseer.ist.psu.edu/kaushik93algebraic.html More
@inproceedings{ kaushik92algebraic,
author = "Kaushik and Sharma and Huang and Johnson and Johnson and Sadayappan",
title = "An Algebraic Theory for Modeling Multistage Interconnection Networks",
booktitle = "{ICPADS}: International Conference on Parallel and Distributed Systems, National Tsing Hua University, Hsinchu, Taiwan, Republic of China",
year = "1992",
url = "citeseer.ist.psu.edu/kaushik93algebraic.html" }
Citations (may not include all citations):326 Topics in Matrix Analysis (context) - Horn, Johnson - 1991
140 Kronecker Products and Matrix Calculus: With Applications (context) - Graham - 1981
135 Computational Framework for the Fast Fourier Transform (context) - Van Loan - 1992
117 Access and alignment of data in an array processor (context) - Lawrie - 1975
93 Parallel processing with the perfect shuffle (context) - Stone - 1971
74 Design of a massively parallel processor (context) - Batcher - 1980
58 Interconnection Networks for Large Scale Parallel Processing.. (context) - Siegel - 1990
57 A survey of interconnection networks (context) - Feng - 1981
46 a class of multistage interconnection networks (context) - Wu, Feng - 1980
22 cube microprocessor array (context) - The, n- - 1977
17 IEEE Transactions on Computers (context) - Davio, shuffle - 1981
17 Interconnection networks for SIMD machines (context) - Siegel - 1979
13 modifying and implementing Fourier transform algorithms on v.. (context) - Johnson, Johnson et al. - 1990
13 The flip network in STARAN (context) - Batcher - 1976
11 Multilinear algebra and parallel programming (context) - Johnson, Huang et al. - 1991
11 Generating parallel programs from tensor product formulas: a.. (context) - Huang, Johnson et al. - 1992
10 exchange-type switching networks (context) - Parker, shuffle - 1980
9 Graph theoretical analysis and design of multistage intercon.. (context) - Agrawal - 1983
8 The universality of the shuffle-exchange network (context) - Wu, Feng - 1981
7 The reverse exchange interconnection network (context) - Wu, Feng - 1980
7 A model of SIMD machines and a comparison of various interco.. (context) - Siegel - 1979
7 A tensor product formulation of Strassen's matrix multiplica.. - Huang, Johnson et al. - 1990
5 Bit serial parallel processing systems (context) - Batcher - 1982
4 Data manipulating functions in parallel processors and their.. (context) - Feng - 1974
3 Tensor permutations and block matrix allocation (context) - Johnson, Huang et al. - 1992
3 Proving the rearrangeability of connecting networks by group.. (context) - Benes - 1975
3 The theory underlying the partitioning of permutation networ.. (context) - Siegel - 1980
2 Towards a group-theoretic proof of the rearrangeability theo.. (context) - Benes - 1975
2 An algebraic theory for modelling direct interconnection net.. (context) - Kaushik, Sharma et al. - 1992
2 Interconnections between processors and memory modules using.. (context) - Lang - 1976
2 An introduction to the multistage cube family of interconnec.. (context) - Siegel, Hsu et al. - 1987
2 A uniform representation of single- and multistage interconn.. (context) - Pradhan, Kodandapani - 1980
1 Applications of group theory to connecting networks (context) - Benes - 1975
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