Novel $\varepsilon$ -Approximation to Data Streams in Sensor Networks

Abstract

We are gradually moving into a realm where sensors, processors, memory and wireless transceivers would be seamlessly integrated together in the physical world and form a wireless sensor network. Such networks pose new challenges in data processing and transmission due to the characteristic of limited communication bandwidth and other resource constraints of sensor networks. To reduce the cost of storage, transmission and processing of time series data generated by sensor nodes, the need for more compact representations of time series data is compelling. Although a large number of data compression algorithms have been proposed to reduce data volume, their offline characteristic or super-linear time complexity prevents them from being applied directly on time series data generated by sensor nodes. Motivated by these observations, we propose an optimal online algorithm GDPLA for constructing a disconnected piecewise linear approximation of a time series which guarantees that the vertical distance between each real data point and the corresponding fit line is less than or equal to $\varepsilon$ . GDPLA not only generates the minimum number of segments to approximate a time series with precision guarantee, but also only requires linear time $O(n)$ bounded by a constant coefficient $6$ , where unit $1$ denotes the time complexity of comparing the slopes of two lines. The low cost characteristic of our method makes it a proper choice for resource-constrained WSNs. Extensive experiments on two real data sets have been conducted to demonstrate the superior compression performance of our method.