SIAM Journal on Computing
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
List ranking and list scan on the Cray C90
Journal of Computer and System Sciences
Better trade-offs for parallel list ranking
Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures
A Simple Optimal List Ranking Algorithm
HIPC '98 Proceedings of the Fifth International Conference on High Performance Computing
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A parallel algorithm with super-linear speed-up for determining the structure of permutations of n elements for extremely large n is presented and analyzed. The algorithm uses sublinear space. If evaluating a randomly chosen successor oracle π costs c time, then a complete analysis can be performed in expected time c ċ (ln n - ln (P ċ N)) ċ n/P, where P is the number of available processors, and N gives the size of the secondary memory of each of the processors. A simple refinement reduces this time by a factor 1 - 1/e. The theoretical analyses are compared with experiments. At the current state of the technology values of n up to about 248 might be handled. We also describe how to perform a screening of π in much less time. If π√n/(In n.P) can be constructed, then such a screening can be performed in O(c ċ √In n ċ n/P) time.