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)


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.


Minimum Element Query Time Space Usage Lower Envelope Additional Space 
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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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