Sorting in c log n parallel steps
Combinatorica
Handbook of theoretical computer science (vol. A)
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Highly fault-tolerant sorting circuits
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SIAM Journal on Computing
A hypercubic sorting network with nearly logarithmic depth
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Lower bounds for merging on the hypercube
CIAC '94 Proceedings of the second Italian conference on Algorithms and complexity
Bounds on the size of merging networks
Discrete Applied Mathematics
Lower bounds for sorting networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
The asymptotic complexity of merging networks
Journal of the ACM (JACM)
A Method of Constructing Selection Networks with O(log n) Depth
SIAM Journal on Computing
Shifting Graphs and Their Applications
Journal of the ACM (JACM)
Lower Bounds on Merging Networks
Journal of the ACM (JACM)
A Probabilistic Selection Network with Butterfly Networks
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Fault-tolerant sorting networks
Fault-tolerant sorting networks
IEEE Transactions on Computers
A (fairly) simple circuit that (usually) sorts
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Halvers and expanders (switching)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Sorting networks and their applications
AFIPS '68 (Spring) Proceedings of the April 30--May 2, 1968, spring joint computer conference
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We study comparator networks for selection, merging, and sorting that output the correct result with high probability, given a random input permutation. We prove tight bounds, up to constant factors, on the size and depth of probabilistic (n,k)-selection networks. In the case of (n, n/2)-selection, our result gives a somewhat surprising bound of $\Theta(n \log \log n)$ on the size of networks of success probability in $[\delta, 1-1/\mbox{poly}(n)]$ , where 驴 is an arbitrarily small positive constant, thus comparing favorably with the best previously known solutions, which have size $\Theta(n\log n)$ . We also prove tight bounds, up to lower-order terms, on the size and depth of probabilistic merging networks of success probability in $[\delta, 1-1/\mbox{poly}(n)]$ , where 驴 is an arbitrarily small positive constant. Finally, we describe two fairly simple probabilistic sorting networks of success probability at least $1-1/\mbox{poly}(n)$ and nearly logarithmic depth.