Encoding 2D Range Maximum Queries

  • Mordecai Golin
  • John Iacono
  • Danny Krizanc
  • Rajeev Raman
  • S. Srinivasa Rao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)


We consider the two-dimensional range maximum query (2D-RMQ) problem: given an array A of ordered values, to pre-process it so that we can find the position of the largest element in a (user-specified) range of rows and range of columns. We focus on determining the effective entropy of 2D-RMQ, i.e., how many bits are needed to encode A so that 2D-RMQ queries can be answered without access to A. We give tight upper and lower bounds on the expected effective entropy for the case when A contains independent identically-distributed random values, and new upper and lower bounds for arbitrary A, for the case when A contains few rows. The latter results improve upon upper and lower bounds by Brodal et al. (ESA 2010). We also give some efficient data structures for 2D-RMQ whose space usage is close to the effective entropy.


Random Input Space Usage Arithmetic Code Lower Common Ancestor Auxiliary Structure 
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 2011

Authors and Affiliations

  • Mordecai Golin
    • 1
  • John Iacono
    • 2
  • Danny Krizanc
    • 3
  • Rajeev Raman
    • 4
  • S. Srinivasa Rao
    • 5
  1. 1.Hong Kong University of Science and TechnologyHong Kong
  2. 2.Polytechnic Institute of New York UniversityUSA
  3. 3.Wesleyan UniversityUSA
  4. 4.University of LeicesterUSA
  5. 5.Seoul National UniversityKorea

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