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Two Dimensional Range Minimum Queries and Fibonacci Lattices

  • Gerth Stølting Brodal
  • Pooya Davoodi
  • Moshe Lewenstein
  • Rajeev Raman
  • Satti Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)

Abstract

Given a matrix of size N, two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique—the discrepancy properties of Fibonacci lattices—we give an indexing data structure for 2D-RMQs that uses O(N/c) bits additional space with O(clogc(loglogc)2) query time, for any parameter c, 4 ≤ c ≤ N. Also, when the entries of the input matrix are from {0,1}, we show that the query time can be improved to O(clogc) with the same space usage.

Keywords

Minimum Element Query Time Space Usage Lower Envelope Additional Space 
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-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gerth Stølting Brodal
    • 1
  • Pooya Davoodi
    • 2
  • Moshe Lewenstein
    • 3
  • Rajeev Raman
    • 4
  • Satti Srinivasa Rao
    • 5
  1. 1.MADALGOAarhus UniversityDenmark
  2. 2.Polytechnic Institute of New York UniversityUnited States
  3. 3.Bar-Ilan UniversityIsrael
  4. 4.University of LeicesterUK
  5. 5.Seoul National UniversityS. Korea

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