Adaptive spatial partitioning for multidimensional data streams

We propose a space-efficient scheme for summarizing multidimensional data streams. Our sketch can be used to solve spatial versions of several classical data stream queries efficiently. For instance, we can track epsilon-hot spots, which are congruent boxes containing at least an epsilon fraction of the stream, and maintain hierarchical heavy hitters in d dimensions. Our sketch can also be viewed as a multidimensional generalization of the epsilon-approximate quantile summary. The space complexity of our scheme is O((1/epsilon) log R) if the points lie in the domain [0, R](d), where d is assumed to be a constant. The scheme extends to the sliding window model with a log (epsilon n) factor increase in space, where n is the size of the sliding window. Our sketch can also be used to answer epsilon-approximate rectangular range queries over a stream of d-dimensional points.