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Sampling based algorithms for quantile computation in sensor networks

We study the problem of computing approximate quantiles in large-scale sensor networks communication-efficiently, a problem previously studied by Greenwald and Khana [12] and Shrivastava et al [21]. Their algorithms have a total communication cost of O(k log2 n / ε) and O(k log u / ε), respectively, where k is the number of nodes in the network, n is the total size of the data sets held by all the nodes, u is the universe size, and ε is the required approximation error. In this paper, we present a sampling based quantile computation algorithm with O(√kh/ε) total communication (h is the height of the routing tree), which grows sublinearly with the network size except in the pathological case h=Θ(k). In our experiments on both synthetic and real data sets, this improvement translates into a 10 to 100-fold communication reduction for achieving the same accuracy in the computed quantiles. Meanwhile, the maximum individual node communication of our algorithm is no higher than that of the previous two algorithms.