We consider the problem of tracking quantiles and range countings in wireless sensor networks. The quantiles and range countings are two important aggregations to characterize a data distribution. Let S(t) = (d 1 , . . . , d n ) denote the multi-set of sensory data that have arrived until time t, which is a sequence of data orderly collected by nodes s 1 , s 2 , . . . , s k . One of our goals is to continuously track -approximate φ-quantiles (0 ≤ φ ≤ 1) of S(t) for all φ's with efficient total communication cost and balanced individual communication cost. The other goal is to track ( , δ)-approximate range countings satisfying the requirement of arbitrary precision specified by different users. In this paper, a deterministic tracking algorithm based on a dynamic binary tree is proposed to track where k is the number of the nodes in a network, n is the total number of the data, and is the user-specified approximation error. For range countings, a Bernoulli sampling based algorithm is proposed to track ( , δ)-approximate range countings, whose total communication cost is O ( +n c ), where δ is the user-specified error probability, n c is the number of clusters.
Approximate aggregation for tracking quantiles and range countings is presented in REF , where a dynamic binary tree based deterministic tracking algorithm is proposed.