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Oil spill at
time t 2
Oil spill at
time t 1
Oil Spill
detected
at time t
0
Figure 7.4. Spread of an oil spill detected in the water over time [92].
data distributions) are grouped together, using the hierarchical organi-
zation of the WSN. Each group corresponds to a homogeneous region in
space, whose boundaries can be effectively approximated. Then, we can
track the movements of these regions over time in a distributed manner,
keeping awake only the sensors that are close to the regions that are
being tracked. This process is eciently implemented by tracking the
movement of the boundaries of each region.
3.3 Outlier Detection
The second application, which we examine in more detail, is dis-
tributed deviation detection in a sensor network. The goal is to identify
values (or the corresponding sensor nodes) that look very different from
their spatio-temporal neighbors (i.e., the values in the recent history of
the sensor stream, or the values in the streams of spatially close sensors).
We note that this is a challenging problem, even for static datasets.
This problem is important in a WSN setting because it can be used
to identify faulty sensors, and to filter spurious reports from different
sensors. Even if we are certain of the quality of measurements reported
by the sensors, the identification of outliers provides an ecient way to
focus on the interesting events in the sensor network.
In the following subsections, we describe the approaches that have
been proposed in the literature, separating them in approximate and
exact , according to whether they provide guarantees on the detection of
all the outliers.
3.3.1 Approximate Approaches. We first examine outlier
identification techniques that cannot provide any hard guarantees on the
 
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