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 N(2 log N-1) control complexity of the N/spl 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 2log K+2 depth rearrangeable network called K-Benes for routing K-bounded permutations with control 2N log K, 0/spl les/K/spl les/N/4. We then show that the N/spl times/N Benes network itself (with one additional stage) contains every KR-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 2log K+2 and, therefore, the K-Benes (and, hence, the KR-Benes) is optimal.