Improved Algorithms for Time Decay Streams
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In the time-decay model for data streams, elements of an underlying data set arrive sequentially with the recently arrived elements being more important. A common approach for handling large data sets is to maintain a coreset, a succinct summary of the processed data that allows approximate recovery of a predetermined query. We provide a general framework that takes any offline-coreset and gives a time-decay coreset for polynomial time decay functions. We also consider the exponential time decay model for k-median clustering, where we provide a constant factor approximation algorithm that utilizes the online facility location algorithm. Our algorithm stores O(k(hΔ)+h) points where h is the half-life of the decay function and Δ is the aspect ratio of the dataset. Our techniques extend to k-means clustering and M-estimators as well.
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