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The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network
The Benes network has been used as a rearrangeable network for over 40 years,
yet the uniform control complexity of the Benes is
not optimal for many permutations. In this paper, we present a novel depth rearrangeable network called KR-Benes that is {\it
permutation-specific control-optimal}. The KR-Benes routes {\it every}
permutation with the minimal control complexity {\it 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
depth rearrangeable network called -Benes for routing
-bounded permutations with control , . We then
show that the Benes network itself (with one additional stage)
contains every -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
-bounded permutations must have depth , and therefore the
-Benes (and hence the KR-Benes) is optimal.Comment: 18 pages, 11 figures, website http://www.csc.lsu.edu/~rkannan V3:
Proved the (previous) Conjecture on Optimality of K-Bene