Approximate Aggregation for Tracking Quantiles in Wireless Sensor Networks

Abstract

We consider the problem of tracking quantiles in wireless sensor networks with efficient communication cost. Compared with the algebraic aggregations such as Sum, Count, or Average, holistic aggregations such as quantiles can better characterize data distribution. Let \(S(t) = (d_1, \ldots , d_n)\) be the multi-set of sensory data that have arrived until time \(t\) in the entire network, which is a sequence of data orderly collected by nodes \(s_1, s_2, \ldots , s_k\). The goal is to continuously track \(\epsilon \)-approximate \(\phi \)-quantiles \((0 \le \phi \le 1)\) of \(S(t)\) at the sink for all \(\phi \)’s with efficient total communication cost and balanced individual communication cost. In this paper, a deterministic tracking algorithm based on a dynamic binary tree is proposed to track \(\epsilon \)-approximate \(\phi \)-quantiles \((0 \le \phi \le 1)\) in wireless sensor networks, whose total communication cost is \(O(k / \epsilon \cdot \log n \cdot \log ^2 (1 / \epsilon ))\), where \(k\) is the number of the nodes in a network, \(n\) is the total number of the data items, and \(\epsilon \) is the required approximation error.