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<p>Many routing problems in parallel processing, such as concentration and permutationproblems, can be cast as sorting problems. In this paper, we consider the problem ofsorting on a new model, called an adaptive sorting network. We show that any sequenceof n bits can be sorted on this model in O(lg/sup 2/ n) bit-level delay using O(n) constantfanin gates. This improves the cost complexity of K.E. Batcher's binary sorters (1968) bya factor of O(lg/sup 2/ n) while matching their sorting time. The only other network thatcan sort binary sequences in O(n) cost is the network version of columnsort algorithm,but this requires excessive pipelining. In addition, using binary sorters, we constructpermutation networks with O(n lg n) bit-level cost and O(lg/sup 3/ n) bit-level delay.These results provide the asymptotically least-cost practical concentrators andpermutation networks to date. We note, of course, that the well-known AKS sortingnetwork has O(lg n) sorting time and O(n lg n) cost, but the constants hidden in thesecomplexities are so large that our complexities outperform those of the AKS sortingnetwork until n becomes extremely large.</p>
Index Termssorting; parallel algorithms; communication complexity; binary sequences; adaptive binary sorting schemes; interconnection networks; routing problems; parallel processing; concentration; permutation problems; sorting problems; cost complexity; permutation networks; AKS sorting network

M. Chien and A. Yavuz Oruc, "Adaptive Binary Sorting Schemes and Associated Interconnection Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 561-572, 1994.
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