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The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network
May 2005 (vol. 54 no. 5)
pp. 534-544
ASCII Text
x 
 
Rajgopal Kannan, "The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network," IEEE Transactions on Computers, vol. 54, no. 5, pp. 534-544, May, 2005.
 
 
BibTex
x
 
@article{ 10.1109/TC.2005.84,
author = {Rajgopal Kannan},
title = {The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network},
journal ={IEEE Transactions on Computers},
volume = {54},
number = {5},
issn = {0018-9340},
year = {2005},
pages = {534-544},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2005.84},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network
IS - 5
SN - 0018-9340
SP534
EP544
EPD - 534-544
A1 - Rajgopal Kannan,
PY - 2005
KW - Benes network
KW - rearrangeability
KW - optimal control algorithm.
VL - 54
JA - IEEE Transactions on Computers
ER -
 
Web Extra: View supplemental material
The Benes network has been used as a rearrangeable network for over 40 years, yet the uniform N(2 \log N-1) control complexity of the N \times N Benes is not optimal for many permutations. In this paper, we present a novel O(\log N) depth rearrangeable network, called KR-Benes, that is permutation-specific control-optimal. The KR-Benes routes every permutation with the minimal control complexity specific to that permutation and its worst-case complexity for arbitrary permutations is bounded by the Benes; thus, it replaces the Benes when considering control complexity/latency. We design the KR-Benes by first constructing a restricted 2 \log K +2 depth rearrangeable network called K{\hbox{-}}{\rm Benes} for routing K{\hbox{-}}{\rm bounded} permutations with control 2N \log K, 0 \leq K \leq N/4. We then show that the N \times N Benes network itself (with one additional stage) contains every K{\hbox{-}}{\rm Benes} network as a subgraph and use this property to construct the KR-Benes network. With regard to the control-optimality of the KR-Benes, we show that any optimal network for rearrangeably routing K{\hbox{-}}{\rm bounded} permutations must have depth 2 \log K + 2 and, therefore, the K{\hbox{-}}{\rm Benes} (and, hence, the KR-Benes) is optimal.

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Index Terms:
Benes network, rearrangeability, optimal control algorithm.
Citation:
Rajgopal Kannan, "The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network," IEEE Transactions on Computers, vol. 54, no. 5, pp. 534-544, May 2005, doi:10.1109/TC.2005.84
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