  In many emerging applications, data streams are monitored in a network
environment. Due to limited communication bandwidth and other resource
constraints, a critical and practical demand is to online compress data streams
continuously with quality guarantee. Although many data compression and digital
signal processing methods have been developed to reduce data volume, their
super-linear time and more-than-constant space complexity prevents them from
being applied directly on data streams, particularly over resource-constrained
sensor networks. In this paper, we tackle the problem of online quality
guaranteed compression of data streams using fast linear approximation (i.e.,
using line segments to approximate a time series). Technically, we address two
versions of the problem which explore quality guarantees in different forms. We
develop online algorithms with linear time complexity and constant cost in
space. Our algorithms are optimal in the sense they generate the minimum number
of segments that approximate a time series with the required quality guarantee.
To meet the resource constraints in sensor networks, we also develop a fast
algorithm which creates connecting segments with very simple computation. The
low cost nature of our methods leads to a unique edge on the applications of
massive and fast streaming environment, low bandwidth networks, and heavily
constrained nodes in computational power. We implement and evaluate our methods
in the application of an acoustic wireless sensor network.
