Maintenance of multidimensional histograms

Shanmugavelayutham Muthukrishnan, Martin Strauss

    Research output: Contribution to journalArticle

    Abstract

    We present a space- and time- efficient algorithm for maintaining multidimensional histograms for data that is dynamic, i.e., subject to updates that may be increments or decrements. Both space used as well as per-update and computing times are polylogarithmic in the input data size; this is the first known algorithm in the data stream model for this problem with this property. One of the powerful motivation for studying data stream algorithms is in analyzing traffic log from IP networks where d-dimensional data (for small d) is common. Hence, our results are of great interest. The result itself is achieved by generalizing methods known for maintenance of unidimensional histograms under updates - finding significant tensor generalizations of one dimensional wavelets, approximating distributions by robust representations - and relationships amongst histograms such as those between tensor wavelets or hierarchical histograms and general histograms.

    Original languageEnglish (US)
    Pages (from-to)352-362
    Number of pages11
    JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2914
    StatePublished - Dec 1 2003

    Fingerprint

    Histogram
    Maintenance
    Tensors
    Update
    Data Streams
    Wavelets
    Tensor
    IP Networks
    Increment
    Efficient Algorithms
    Traffic
    Computing
    Model

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Maintenance of multidimensional histograms. / Muthukrishnan, Shanmugavelayutham; Strauss, Martin.

    In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2914, 01.12.2003, p. 352-362.

    Research output: Contribution to journalArticle

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