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Range Minimum Query Indexes in Higher Dimensions

  • Pooya Davoodi
  • John Iacono
  • Gad M. Landau
  • Moshe Lewenstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)

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.

Keywords

Reduction Technique Minimum Element Query Time Dimensional Array Lower Common Ancestor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Pooya Davoodi
    • 1
  • John Iacono
    • 1
  • Gad M. Landau
    • 1
    • 2
  • Moshe Lewenstein
    • 3
  1. 1.Polytechnic Institute of New York UniversityNew YorkUSA
  2. 2.Haifa UniversityHaifaIsrael
  3. 3.Bar-Ilan UniversityRamat GanIsrael

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