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As data gathering grows easier, and as researchers discover new ways to interpret data, streaming-data algorithms have become essential in many elds. Data stream computation precludes algorithms that require random access or large memory. In this paper, we consider the problem of clustering data streams, which is important in the analysis a variety of… (More)

The data stream model has recently attracted attention for its applicability to numerous types of data, including telephone records, web documents and clickstreams. For analysis of such data, the ability to process the data in a single pass, or a small number of passes, while using little memory, is crucial. We describe such a streaming algorithm that… (More)

We study clustering problems in the streaming model, where the goal is to cluster a set of points by making one pass (or a few passes) over the data using a small amount of storage space. Our main result is a randomized algorithm for the <i>k</i>--Median problem which produces a constant factor approximation in one pass using storage space <i>O(k poly</i>… (More)

The sliding window model is useful for discounting stale data in data stream applications. In this model, data elements arrive continually and only the most recent <i>N</i> elements are used when answering queries. We present a novel technique for solving two important and related problems in the sliding window model---maintaining variance and maintaining a… (More)

Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA).… (More)

We consider the problem of estimating the length of a shortest path in a DAG whose edge lengths are known only approximately but can be determined exactly at a cost. Initially, each edge e is known only to lie within an interval le; h e; the estimation algorithm can pay ce to nd the exact length of e. In particular, we study the problem of nding the… (More)

We are given a graph with edge weights, that represents the metric on the vertices in which the distance between two vertices is the total weight of the lowest-weight path between them. Consider the problem of representing this metric using as few edges as possible, provided that new \steiner" vertices (and edges incident on them) can be added. The… (More)

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