TACT Tunable Availability and Consistency Tradeoff for 机智的可调谐的可性和一致性的权衡.pptVIP

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TACT Tunable Availability and Consistency Tradeoff for 机智的可调谐的可性和一致性的权衡.ppt

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TACT Tunable Availability and Consistency Tradeoff for 机智的可调谐的可性和一致性的权衡

A Space-Optimal Data-Stream Algorithm for Coresets in the Plane Extent Measures Diameter, width, convex hull Simple shapes that enclose point sets Min-radius ball, min-volume box, min-radius cylinder Min-width cylindrical shell, min-width spherical shell Maintaining shape descriptors for moving points Applications Computer graphics Solid modeling Machine learning Data mining Sensor networks Approximation ε-Kernel [A., Har-Peled, Varadarajan,04] Approximation ε-Kernel [A., Har-Peled, Varadarajan,04] This talk: maintaining an ε-kernel Q of a stream S of points Results Previous results Our main result: a space-optimal data-stream algorithm in R2 O(1/ε1/2) space, O(log 1/ε) update time (amortized) Algorithm Overview Problem is easy if point set is fat Algorithm Overview Problem is easy if point set is fat Algorithm Overview Problem is easy if point set is fat Keep track of nearest neighbor of each grid point Can be implemented efficiently in O(log 1/ε) time per point Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Epochs and subepochs Algorithm Overview Chan’s algorithm Algorithm Overview Chan’s algorithm Algorithm Overview Chan’s algorithm Algorithm Overview Chan’s algorithm Algorithm Overview Chan’s algorithm Total space: (1/ε1/2) log2(1/ε) New Ingredient Prune points of previous epochs at the beginning of each new epoch New Ingredient Prune points of previous epochs at the beginning of each new epoch Ne