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- W2949664872 abstract "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 {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 $2 log K +2$ depth rearrangeable network called $K$-Benes for routing $K$-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 $K$-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 $K$-bounded permutations must have depth $2 log K + 2$, and therefore the $K$-Benes (and hence the KR-Benes) is optimal." @default.
- W2949664872 created "2019-06-27" @default.
- W2949664872 creator A5042560222 @default.
- W2949664872 date "2003-09-06" @default.
- W2949664872 modified "2023-09-27" @default.
- W2949664872 title "The KR-Benes Network: A Control-Optimal Rearrangeable Permutation Network" @default.
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