Comparing data streams using Hamming norms (how to zero in)

Graham Cormode, Mayur Datar, Piotr Indyk, S. Muthukrishnan

    Research output: Contribution to journalArticlepeer-review


    Massive data streams are now fundamental to many data processing applications. For example, Internet routers produce large scale diagnostic data streams. Such streams are rarely stored in traditional databases and instead must be processed "on the fly" as they are produced. Similarly, sensor networks produce multiple data streams of observations from their sensors. There is growing focus on manipulating data streams and, hence, there is a need to identify basic operations of interest in managing data streams, and to support them efficiently. We propose computation of the Hamming norm as a basic operation of interest. The Hamming norm formalizes ideas that are used throughout data processing. When applied to a single stream, the Hamming norm gives the number of distinct items that are present in that data stream, which is a statistic of great interest in databases. When applied to a pair of streams, the Hamming norm gives an important measure of (dis)similarity: the number of unequal item counts in the two streams. Hamming norms have many uses in comparing data streams. We present a novel approximation technique for estimating the Hamming norm for massive data streams; this relies on what we call the "l0 sketch" and we prove its accuracy. We test our approximation method on a large quantity of synthetic and real stream data, and show that the estimation is accurate to within a few percentage points.

    Original languageEnglish (US)
    Pages (from-to)529-540
    Number of pages12
    JournalIEEE Transactions on Knowledge and Data Engineering
    Issue number3
    StatePublished - May 2003


    • Approximate query processing
    • Data reduction
    • Data stream analysis
    • Data structures and algorithms

    ASJC Scopus subject areas

    • Information Systems
    • Computer Science Applications
    • Computational Theory and Mathematics


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