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Index Transformation Algorithms in a Linear Algebra Framework
KTH, School of Computer Science and Communication (CSC), Centres, Centre for High Performance Computing, PDC. (Parallelldatorcentrum)
1994 (English)In: IEEE Transactions on Parallel and Distributed Systems, ISSN 1045-9219, E-ISSN 1558-2183, Vol. 5, no 12, 1302-1309 p.Article in journal (Refereed) Published
Abstract [en]

We present a linear algebraic formulation for a class of index transformations such as Gray code encoding and decoding, matrix transpose, bit reversal, vector reversal, shuffles, and other index or dimension permutations. This formulation unifies, simplifies, and can be used to derive algorithms for hypercube multiprocessors. We show how all the widely known properties of Gray codes, and some not so well-known properties as well, can be derived using this framework. Using this framework, we relate hypercube communications algorithms to Gauss-Jordan elimination on a matrix of 0's and 1's.

Place, publisher, year, edition, pages
1994. Vol. 5, no 12, 1302-1309 p.
Keyword [en]
BINARY-COMPLEMENT PERMUTE; BINARY HYPERCUBE; CONNECTION MACHINE; GRAY CODE; INDEX TRANSFORMATION; MULTIPROCESSOR COMMUNICATION; ROUTING; SHUFFLE
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-90985DOI: 10.1109/71.334903OAI: oai:DiVA.org:kth-90985DiVA: diva2:507635
Note
NR 20140805Available from: 2012-03-05 Created: 2012-03-05 Last updated: 2017-12-07Bibliographically approved

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