Estimating entropy and entropy norm on data streams

Amit Chakrabarti, Khanh Do Ba, S. Muthukrishnan

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We consider the problem of computing information-theoretic functions, such as entropy, on a data stream, using sublinear space. Our first result deals with a measure we call the entropy norm of an input stream: it is closely related to entropy but is structurally similar to the well-studied notion of frequency moments. We give a polylogarithmic-space, one-pass algorithm for estimating this norm under certain conditions on the input stream. We also prove a lower bound that rules out such an algorithm if these conditions do not hold. Our second group of results is for estimating the empirical entropy of an input stream. We first present a sublinear-space, one-pass algorithm for this problem. For a stream of m items and a given real parameter α, our algorithm uses space Õ(m) and provides an approximation of 1/α in the worst case and (1+ε) in “most” cases. We then present a two-pass, polylogarithmic-space, (1+ε)-approximation algorithm. All our algorithms are quite simple.

    Original languageEnglish (US)
    Pages (from-to)63-78
    Number of pages16
    JournalInternet Mathematics
    Volume3
    Issue number1
    DOIs
    StatePublished - Jan 1 2006

    ASJC Scopus subject areas

    • Modeling and Simulation
    • Computational Mathematics
    • Applied Mathematics

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