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)

Abstract

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.

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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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