New lower bounds for parallel computation
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Efficient sampling of random permutations
Journal of Discrete Algorithms
The average complexity of deterministic and randomized parallel comparison sorting algorithms
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Cascading divide-and-conquer: A technique for designing parallel algorithms
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Randomized Shellsort: a simple oblivious sorting algorithm
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Randomized Shellsort: A Simple Data-Oblivious Sorting Algorithm
Journal of the ACM (JACM)
A bibliography on computational molecular biology and genetics
Mathematical and Computer Modelling: An International Journal
More efficient parallel integer sorting
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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We assume a parallel RAM model which allows both concurrent writes and concurrent reads of global memory. Our algorithms are randomized: each processor is allowed an independent random number generator. However our stated resource bounds hold for worst case input with overwhelming likelihood as the input size grows. We give a new parallel algorithm for integer sorting where the integer keys are restricted to at most polynomial magnitude. Our algorithm costs only logarithmic time and is the first known where the product of the time and processor bounds are bounded by a linear function of the input size. These simultaneous resource bounds are asymptotically optimal. All previous known parallel sorting algorithms required at least a linear number of processors to achieve logarithmic time bounds, and hence were nonoptimal by at least a logarithmic factor.