Compressed range minimum queries

Seungbum Jo, Shay Mozes, Oren Weimann

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


Given a string S of n integers in [0,σ), a range minimum query RMQ(i, j) asks for the index of the smallest integer in S[i…j]. It is well known that the problem can be solved with a succinct data structure of size 2n + o(n) and constant query-time. In this paper we show how to preprocess S into a compressed representation that allows fast range minimum queries. This allows for sublinear size data structures with logarithmic query time. The most natural approach is to use string compression and construct a data structure for answering range minimum queries directly on the compressed string. We investigate this approach using grammar compression. We then consider an alternative approach. Even if S is not compressible, its Cartesian tree necessarily is. Therefore, instead of compressing S using string compression, we compress the Cartesian tree of S using tree compression. We show that this approach can be exponentially better than the former, and is never worse by more than an O(σ) factor (i.e. for constant alphabets it is never asymptotically worse).

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings
EditorsTravis Gagie, Alistair Moffat, Gonzalo Navarro, Ernesto Cuadros-Vargas
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783030004781
StatePublished - 2018
Event25th International Symposium on String Processing and Information Retrieval, SPIRE 2018 - Lima, Peru
Duration: 9 Oct 201811 Oct 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11147 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference25th International Symposium on String Processing and Information Retrieval, SPIRE 2018

Bibliographical note

Publisher Copyright:
© Springer Nature Switzerland AG 2018.


  • Cartesian tree
  • Grammar compression
  • RMQ
  • SLP
  • Tree compression

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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