Improved range-summable random variable construction algorithms

A. R. Calderbank, A. Gilbert, K. Levchenko, Shanmugavelayutham Muthukrishnan, M. Strauss

    Research output: Contribution to conferencePaper

    Abstract

    Range-summable universal hash functions, also known as range-summable random variables, are binary-valued hash functions which can efficiently hash single values as well as ranges of values from the domain. They have found several applications in the area of data stream processing where they are used to construct sketches - small-space summaries of the input sequence. We present two new constructions of range-summable universal hash functions on n-bit strings, one based on Reed-Muller codes which gives k-universal hashing using O(n log k) space arid time for point operations and O(n 2 1og k) for range operations, and another based on a new subcode of the second-order Reed-Muller code, which gives 5-universal hashing using O(n) space, O(n log 3 n) time for point operations, and O(n 3) time for range operations. We also present a new sketch data structure using the new hash functions which improves several previous results.

    Original languageEnglish (US)
    Pages840-849
    Number of pages10
    StatePublished - Jul 1 2005
    EventSixteenth Annual ACM-SIAM Symposium on Discrete Algorithms - Vancouver, BC, United States
    Duration: Jan 23 2005Jan 25 2005

    Other

    OtherSixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
    CountryUnited States
    CityVancouver, BC
    Period1/23/051/25/05

    Fingerprint

    Hash functions
    Random variables
    Random variable
    Hash Function
    Range of data
    Reed-Muller Codes
    Universal Function
    Hashing
    Data structures
    Stream Processing
    K-space
    Data Streams
    Data Structures
    Processing
    Strings
    Binary

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Cite this

    Calderbank, A. R., Gilbert, A., Levchenko, K., Muthukrishnan, S., & Strauss, M. (2005). Improved range-summable random variable construction algorithms. 840-849. Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States.

    Improved range-summable random variable construction algorithms. / Calderbank, A. R.; Gilbert, A.; Levchenko, K.; Muthukrishnan, Shanmugavelayutham; Strauss, M.

    2005. 840-849 Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States.

    Research output: Contribution to conferencePaper

    Calderbank, AR, Gilbert, A, Levchenko, K, Muthukrishnan, S & Strauss, M 2005, 'Improved range-summable random variable construction algorithms', Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States, 1/23/05 - 1/25/05 pp. 840-849.
    Calderbank AR, Gilbert A, Levchenko K, Muthukrishnan S, Strauss M. Improved range-summable random variable construction algorithms. 2005. Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States.
    Calderbank, A. R. ; Gilbert, A. ; Levchenko, K. ; Muthukrishnan, Shanmugavelayutham ; Strauss, M. / Improved range-summable random variable construction algorithms. Paper presented at Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Vancouver, BC, United States.10 p.
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