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- W2067506436 abstract "We consider the problem of computing the minimum of n values, and several well-known generalizations [prefix minima, range minima, and all nearest smaller values (ANSV)] for input elements drawn from the integer domain [1··· s ], where s ≥ n . In this article we give simple and efficient algorithms for all of the preceding problems. These algorithms all take O (log log log s ) time using an optimal number of processors and O ( ns ϵ ) space (for constant ϵ < 1) on the COMMON CRCW PRAM. The best known upper bounds for the range minima and ANSV problems were previously O (log log n ) (using algorithms for unbounded domains). For the prefix minima and for the minimum problems, the improvement is with regard to the model of computation. We also prove a lower bound of Ω(log log n ) for domain size s = 2 Ω(log n log log n ) . Since, for s at the lower end of this range, log log n = Ω(log log log s ), this demonstrates that any algorithm running in o (log log log s ) time must restrict the range of s on which it works." @default.
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- W2067506436 date "1998-08-01" @default.
- W2067506436 modified "2023-09-27" @default.
- W2067506436 title "Triply-Logarithmic Parallel Upper and Lower Bounds for Minimum and Range Minima over Small Domains" @default.
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- W2067506436 doi "https://doi.org/10.1006/jagm.1997.0905" @default.
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