Combinatorica
The complexity of Boolean functions
The complexity of Boolean functions
Sorting in c log n parallel steps
Combinatorica
Tight bounds on the complexity of parallel sorting
IEEE Transactions on Computers
The periodic balanced sorting network
Journal of the ACM (JACM)
Introduction to algorithms
A self-routing permutation network
Journal of Parallel and Distributed Computing
Self-routing and route balancing in connection networks
Self-routing and route balancing in connection networks
Fast self-routing permutation switching on an asymptotically minimum coast network
Fast self-routing permutation switching on an asymptotically minimum coast network
Efficient networks for realizing point-to-point assignments in parallel processors
Efficient networks for realizing point-to-point assignments in parallel processors
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Bounds to Complexities of Networks for Sorting and for Switching
Journal of the ACM (JACM)
PODC '83 Proceedings of the second annual ACM symposium on Principles of distributed computing
Regular Sparse Crossbar Concentrators
IEEE Transactions on Computers
Minimizing Communication in the Bitonic Sort
IEEE Transactions on Parallel and Distributed Systems
An ASIC design and formal analysis of a novel pipelined and parallel sorting accelerator
Integration, the VLSI Journal
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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.