article

Space-Efficient Preprocessing Schemes for Range Minimum Queries on Static Arrays

Authors:

Johannes Fischer,

Volker HeunAuthors Info & Claims

SIAM Journal on Computing, Volume 40, Issue 2

Pages 465 - 492

https://doi.org/10.1137/090779759

Published: 01 April 2011 Publication History

Abstract

Given a static array of $n$ totally ordered objects, the range minimum query problem is to build a data structure that allows us to answer efficiently subsequent on-line queries of the form “what is the position of a minimum element in the subarray ranging from $i$ to $j$?”. We focus on two settings, where (1) the input array is available at query time, and (2) the input array is available only at construction time. In setting (1), we show new data structures (a) of size $\frac{2n}{c(n)}-\Theta\bigl(\frac{n\lg\lg n}{c(n)\lg n}\bigr)$ bits and query time $O(c(n))$ for any positive integer function $c(n)\in O\bigl(n^\varepsilon\bigr)$ for an arbitrary constant $0<\varepsilon<1$, or (b) with $O(nH_k)+o(n)$ bits and $O(1)$ query time, where $H_k$ denotes the empirical entropy of $k$th order of the input array. In setting (2), we give a data structure of size $2n+o(n)$ bits and query time $O(1)$. All data structures can be constructed in linear time and almost in-place.

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cover image SIAM Journal on Computing

SIAM Journal on Computing Volume 40, Issue 2

March 2011

372 pages

ISSN:0097-5397

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Society for Industrial and Applied Mathematics

United States

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Published: 01 April 2011

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