Embedding of binary trees into hypercubes

Journal Article · Thu Jun 01 04:00:00 EDT 1989 · Journal of Parallel and Distributed Computing; (USA)

DOI:https://doi.org/10.1016/0743-7315(89)90013-0· OSTI ID:5242754

Bier, T ^[1]; Loe, K F ^[2]

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1. Dept. of Mathematics, National Univ. of Singapore, Singapore 0511 (SG)
2. Dept. of Information Systems and Computer Science, National Univ. of Singapore, Singapore 0511 (SG)

The authors present a mathematical model of parallel computing in a hypercubical parallel computer. This is based on embedding binary trees or forests into the n-dimensional hypercube. They consider three different models corresponding to three different computing situations. First, they assume that the processing time at each level of the binary tree is arbitrary, and develop the corresponding mathematical model of an embedding of a binary tree into the hypercube. Then they assume that the processing time at each level of the binary tree is the same for all processors involved at that level, and for this they develop the mathematical model of a loop embedding of a binary tree into the hypercube. The most general case is that in which only certain neighboring levels are active. Here they assume for simplicity that only the processors corresponding to two neighboring levels are active at the same time, and correspondingly they develop the mathematical model of a level embedding of a binary tree into the hypercube to cover this case. Both loop embeddings and level embeddings allow the authors to use the same processor several times during the execution of a program.

• OSTI ID: 5242754
• Journal Information: Journal of Parallel and Distributed Computing; (USA), Journal Name: Journal of Parallel and Distributed Computing; (USA) Vol. 6:3; ISSN JPDCE; ISSN 0743-7315
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
COMPUTER CALCULATIONS
COMPUTERS
HYPERCUBE COMPUTERS
MATHEMATICAL MODELS
PARALLEL PROCESSING
PROGRAMMING