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

  • Authors:
  • Johannes Fischer;Volker Heun

  • Affiliations:
  • johannes.fischer@kit.edu;volker.heun@bio.ifi.lmu.de

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2011

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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