Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Deterministic selection in O(loglog N) parallel time
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
A fast probabilistic parallel sorting algorithm
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
The average complexity of deterministic and randomized parallel comparison sorting algorithms
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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We prove a worst case lower bound of Ω(log log n) for randomized algorithms merging two sorted lists of length n in parallel using n processors on Valiant's parallel computation tree model. We show how to strengthen this result to a lower bound for the expected time taken by any algorithm on the uniform distribution. Finally, bounds are given for the average time required for the problem when the number of processors is less than and greater than n.