Sorting in c log n parallel steps
Combinatorica
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A Lower Bound for Sorting Networks Based on the Shuffle Permutation
A Lower Bound for Sorting Networks Based on the Shuffle Permutation
A lower bound for sorting networks based on the shuffle permutation
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
On probabilistic networks for selection, merging, and sorting
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
An O(nlogn)-size fault-tolerant sorting network (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On Probabilistic Networks for Selection, Merging, and Sorting
Theory of Computing Systems
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A natural class of “hypercubic” sorting networks is defined. The regular structure of these sorting networks allows for elegant and efficient implementations on any of the so-called hypercubic networks (e.g., the hypercube, shuffle-exchange, butterfly, and cube-connected cycles). This class of sorting networks contains Batcher's O(lg2 n)-depth bitonic sort, but not the O(lg n)-depth sorting network of Ajtai, Komlo´s, and Szemere´di. In fact, no o(lg2 n)-depth compare-interchange sort was previously known for any of the hypercubic networks. In this paper, we prove the existence of a family of 2O((lg lg n)1/2) lg n-depth hypercubic sorting networks. Note that this depth is o(lg1+&egr; n) for any constant &egr; 0.