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Efficient Routing and Sorting Schemes for de Bruijn Networks
November 1997 (vol. 8 no. 11)
pp. 1157-1170

Abstract—We consider the problems of routing and sorting on a de Bruijn network. First, we show that any deterministic oblivious routing scheme for permutation routing on a d-ary de Bruijn network with N = dn nodes, in the worst case, will take $\Omega (\sqrt N)$ steps under the single-port model. This improves the existing lower bounds provided d is not a constant. We also show that the lower bound is indeed a tight one. Second, we present a deterministic nonoblivious permutation routing algorithm which runs in O(d·n2) time on a d-ary de Bruijn network with N = dn nodes. This algorithm is currently the fastest known nonoblivious deterministic routing algorithm for de Bruijn networks of arbitrary degree. Finally, we present an efficient general sorting algorithm for the de Bruijn networks of arbitrary degree. This algorithm is the best sorting algorithm known so far. It runs in O((log d) ·d·n2) time for directed de Bruijn network with dn nodes, degree d, and diameter n. As a corollary, we show that on a binary de Bruijn network of N nodes, our sorting scheme requires at most 2 log2N steps.

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Index Terms:
Oblivious routing, nonoblivious routing, permutation routing, parallel sorting, de Bruijn network.
Citation:
D. Frank Hsu, David S.L. Wei, "Efficient Routing and Sorting Schemes for de Bruijn Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 8, no. 11, pp. 1157-1170, Nov. 1997, doi:10.1109/71.642950
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