Range minimum query indexes in higher dimensions

Pooya Davoodi, John Iacono, Gad M. Landau, Moshe Lewenstein

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

Abstract

Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings
EditorsUgo Vaccaro, Ely Porat, Ferdinando Cicalese
PublisherSpringer Verlag
Pages149-159
Number of pages11
ISBN (Print)9783319199283
DOIs
StatePublished - 2015
Event26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy
Duration: 29 Jun 20151 Jul 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9133
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015
Country/TerritoryItaly
CityIschia Island
Period29/06/151/07/15

Bibliographical note

Funding Information:
M. Lewenstein—Research supported by BSF grant 2010437, a Google Research Award and GIF grant 1147/2011.

Funding Information:
J. Iacono—Research supported by NSF grant CCF-1018370 and BSF grant 2010437.

Funding Information:
G.M. Landau—Research partially supported by the National Science Foundation Award 0904246, Israel Science Foundation grant 571/14, Grant No. 2008217 from the United States- Israel Binational Science Foundation (BSF) and DFG.

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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