Abstract
This paper gives 3-page book embeddings of three important interconnection networks: the FFT network, the Benes rearrangeable permutation network, and the barrel shifter network. Since all three networks are eventually nonplanar, they require three pages and the present embeddings are optimal. Also, the embeddings have pages of comparable widths.
The embeddings of the FFT and barrel shifter networks are obtained by decomposing these recursively defined networks into smaller copies of themselves and using induction. The embedding of the Benes network uses a novel decomposition of the network into eight copies of a smaller FFT network.
Similar content being viewed by others
References
V. E. Benes. Optimal rearrangeable multistage connecting networks.Bell Syst. Tech. J., 43 (1964), 1641–1656.
F. Bernhart and P. C. Kainen. The book thickness of a graph.J. Combin. Theory (B), 27 (1979), 320–331.
F. R. K. Chung, F. T. Leighton, and A. L. Rosenberg. Diogenes—A methodology for designing fault-tolerant processor arrays.13th International Conference on Fault-Tolerant Computing, 1983, pp. 26–32.
F. R. K. Chung, F. T. Leighton, and A. L. Rosenberg. Embedding graphs in books: a layout problem with applications to VLSI design. To appear,SIAM Journal on Algebraic and Discrete Methods.
T. Feng. A survey of interconnection networks,Computer, 14 (1981), 12–27.
A. L. Rosenberg. The Diogenes approach to testable fault-tolerant arrays of processors.IEEE Trans. Comput., C-32 (1983), 902–910.
H. S. Stone. Parallel processing with the perfect shuffle.IEEE Trans. Comput., C-20 (1971), 153–161.
Author information
Authors and Affiliations
Additional information
Communicated by F. Thomson Leighton.
This work was accomplished as a part of the MITRE Corporation's Independent Research and Development Program.
Rights and permissions
About this article
Cite this article
Games, R.A. Optimal book embeddings of the FFT, benes, and barrel shifter networks. Algorithmica 1, 233–250 (1986). https://doi.org/10.1007/BF01840445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01840445