Triply-logarithmic upper and lower bounds for minimum, range minima, and related problems with integer inputs

O. Berkman, Y. Matias, P. Ragde

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of computing the minimum of n values, and several well-known generalizations (prefix minima, range minima, and all-ncarest-smallcr-values (ANSV) problems) for input element drawn from the integer domain [1..s] where s ≥ n. Recent work [4] has shown that parallel algorithms that are sensitive to the size of the input domain can improve on more general parallel algorithms. The cited paper demonstrates an O(log log log s)-step algorithm on an n-processor Priority CRCW PRAM for finding the prefix-minima of n numbers in the range [l..s]. The best known upper bounds for the range minima and ANSV problems were previously O(log log n) (using algorithms for general input). This was also the best known upper hound for computing prefix minima or even just the minimum on the COMMON CRCW PRAM; this model has a Ɵ(log n/log log n) time separation from the stronger PRIORITY model when using the same number of processors. In this paper we give simple and efficient algorithms for all of the above problems. These algorithms all take O(log log log s) time using an optimal number of processors and O(nsϵ) space on the Common CRCW PRAM. We also prove a lower bound demonstrating that no algorithm is asymptotically faster as a function of s, by showing that for s = 22Ω(log n log log n) the upper bounds are tight.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings
EditorsFrank Dehne, Jorg-Rudiger Sack, Nicola Santoro, Sue Whitesides
PublisherSpringer Verlag
Pages175-187
Number of pages13
ISBN (Print)9783540571551
DOIs
StatePublished - 1993
Externally publishedYes
Event3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada
Duration: 11 Aug 199313 Aug 1993

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume709 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd Workshop on Algorithms and Data Structures, WADS 1993
Country/TerritoryCanada
CityMontreal
Period11/08/9313/08/93

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