Tight comparison bounds on the complexity of parallel sorting
SIAM Journal on Computing
Parallel Sorting Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Routing, merging and sorting on parallel models of computation
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
The VLSI Complexity of Sorting
IEEE Transactions on Computers
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
An optimal parallel algorithm for integer sorting
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Tight complexity bounds for parallel comparison sorting
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
The complexity of parallel comparison merging
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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In practice, the average time of (deterministic or randomized) sorting algorithms seems to be more relevant than the worst case time of deterministic algorithms. Still, the many known complexity bounds for parallel comparison sorting include no nontrivial lower bounds for the average time required to sort by comparisons n elements with p processors (via deterministic or randomized algorithms). We show that for p ≥ n this time is Θ (log n/log(1 + p/n)), (it is easy to show that for p ≤ n the time is Θ (n log n/p) = Θ (log n/(p/n)). Therefore even the average case behaviour of randomized algorithms is not more efficient than the worst case behaviour of deterministic ones.