Range minimum query indexes in higher dimensions

Pooya Davoodi, John Iacono, Gad M. Landau, Moshe Lewenstein

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

    Abstract

    Range minimum queries (RMQs) are essential in many algorithmic procedures. The problem is to prepare a data structure on an array to allow for fast subsequent queries that find the minimum within a range in the array. We study the problem of designing indexing RMQ data structures which only require sub-linear space and access to the input array while querying. The RMQ problem in one-dimensional arrays is well understood with known indexing data structures achieving optimal space and query time. The two-dimensional indexing RMQ data structures have received the attention of researchers recently. There are also several solutions for the RMQ problem in higher dimensions. Yuan and Atallah [SODA’10] designed a brilliant data structure of size O(N) which supports RMQs in a multi-dimensional array of size N in constant time for a constant number of dimensions. In this paper we consider the problem of designing indexing data structures for RMQs in higher dimensions. We design a data structure of size O(N) bits that supports RMQs in constant time for a constant number of dimensions. We also show how to obtain trade-offs between the space of indexing data structures and their query time.

    Original languageEnglish (US)
    Title of host publicationCombinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings
    PublisherSpringer Verlag
    Pages149-159
    Number of pages11
    Volume9133
    ISBN (Print)9783319199283
    DOIs
    StatePublished - 2015
    Event26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy
    Duration: Jun 29 2015Jul 1 2015

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9133
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    Other26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015
    CountryItaly
    CityIschia Island
    Period6/29/157/1/15

    Fingerprint

    Higher Dimensions
    Data structures
    Query
    Data Structures
    Range of data
    Indexing
    Time Constant
    Multidimensional Arrays
    Linear Space
    Trade-offs

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Davoodi, P., Iacono, J., Landau, G. M., & Lewenstein, M. (2015). Range minimum query indexes in higher dimensions. In Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings (Vol. 9133, pp. 149-159). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_13

    Range minimum query indexes in higher dimensions. / Davoodi, Pooya; Iacono, John; Landau, Gad M.; Lewenstein, Moshe.

    Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Vol. 9133 Springer Verlag, 2015. p. 149-159 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133).

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

    Davoodi, P, Iacono, J, Landau, GM & Lewenstein, M 2015, Range minimum query indexes in higher dimensions. in Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. vol. 9133, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9133, Springer Verlag, pp. 149-159, 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015, Ischia Island, Italy, 6/29/15. https://doi.org/10.1007/978-3-319-19929-0_13
    Davoodi P, Iacono J, Landau GM, Lewenstein M. Range minimum query indexes in higher dimensions. In Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Vol. 9133. Springer Verlag. 2015. p. 149-159. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-19929-0_13
    Davoodi, Pooya ; Iacono, John ; Landau, Gad M. ; Lewenstein, Moshe. / Range minimum query indexes in higher dimensions. Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings. Vol. 9133 Springer Verlag, 2015. pp. 149-159 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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