Deterministic coin tossing with applications to optimal parallel list ranking
Information and Control
SIAM Journal on Computing
Optimal and sublogarithmic time randomized parallel sorting algorithms
SIAM Journal on Computing
A complexity theory of efficient parallel algorithms
Theoretical Computer Science - Special issue: Fifteenth international colloquium on automata, languages and programming, Tampere, Finland, July 1988
Optimal merging and sorting on the EREW PRAM
Information Processing Letters
Improved nonconservative sequential and parallel integer sorting
Information Processing Letters
On parallel hashing and integer sorting
Proceedings of the seventeenth international colloquium on Automata, languages and programming
BLASTING through the information theoretic barrier with FUSION TREES
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Constant-time parallel integer sorting
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Converting high probability into nearly-constant time—with applications to parallel hashing
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
The power of Collision: randomized parallel algorithms for chaining and integer sorting
FST and TC 10 Proceedings of the tenth conference on Foundations of software technology and theoretical computer science
Improved deterministic parallel integer sorting
Information and Computation
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Efficient low-contention parallel algorithms
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Optimal parallel string algorithms: sorting, merging and computing the minimum
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Making deterministic signatures quickly
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Making deterministic signatures quickly
ACM Transactions on Algorithms (TALG)
Subquadratic algorithms for 3SUM
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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We show that n integers in the range 1..n can be stably sorted on an EREW PRAM using O((log n)1/2) time, O(n(log n)1/2(log log n)1/2) operations and O(n) space. In addition, we are able to stably sort n integers in the range 1..n on a deterministic CREW PRAM in O((log n)3/2) time with O(n(log n)1/2) operations and O(n) space and to stably sort n arbitrary integers on a randomized CREW PRAM within the same complexity bounds with high probability. In each case our algorithm is closer to optimality than all previous algorithms for the stated problem in the stated model, and our third result matches the operation count of the best known sequential algorithm. We also show that m integers in the range 1..m can be sorted in O((log n)2) time with O(n) operations on an EREW PRAM using a nonstandard word length of O(log n log log n log m) bits, thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time-processor product, even sequentially. Our algorithms were inspired by, and in one case directly use, the fusion trees recently introduced by Fredman and Willard.