Encoding 2D range maximum queries

Mordecai Golin, John Iacono, Danny Krizanc, Rajeev Raman, S. Srinivasa Rao

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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.

    Original languageEnglish (US)
    Title of host publicationAlgorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings
    Pages180-189
    Number of pages10
    Volume7074 LNCS
    DOIs
    StatePublished - 2011
    Event22nd International Symposium on Algorithms and Computation, ISAAC 2011 - Yokohama, Japan
    Duration: Dec 5 2011Dec 8 2011

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume7074 LNCS
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other22nd International Symposium on Algorithms and Computation, ISAAC 2011
    CountryJapan
    CityYokohama
    Period12/5/1112/8/11

    Fingerprint

    Upper and Lower Bounds
    Encoding
    Entropy
    Query
    Range of data
    Identically distributed
    Data structures
    Data Structures
    Arbitrary

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Golin, M., Iacono, J., Krizanc, D., Raman, R., & Rao, S. S. (2011). Encoding 2D range maximum queries. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings (Vol. 7074 LNCS, pp. 180-189). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS). https://doi.org/10.1007/978-3-642-25591-5_20

    Encoding 2D range maximum queries. / Golin, Mordecai; Iacono, John; Krizanc, Danny; Raman, Rajeev; Rao, S. Srinivasa.

    Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS 2011. p. 180-189 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7074 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Golin, M, Iacono, J, Krizanc, D, Raman, R & Rao, SS 2011, Encoding 2D range maximum queries. in Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. vol. 7074 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7074 LNCS, pp. 180-189, 22nd International Symposium on Algorithms and Computation, ISAAC 2011, Yokohama, Japan, 12/5/11. https://doi.org/10.1007/978-3-642-25591-5_20
    Golin M, Iacono J, Krizanc D, Raman R, Rao SS. Encoding 2D range maximum queries. In Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS. 2011. p. 180-189. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-25591-5_20
    Golin, Mordecai ; Iacono, John ; Krizanc, Danny ; Raman, Rajeev ; Rao, S. Srinivasa. / Encoding 2D range maximum queries. Algorithms and Computation - 22nd International Symposium, ISAAC 2011, Proceedings. Vol. 7074 LNCS 2011. pp. 180-189 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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