2.5 Random trisection approach
Similar to the random bisection approach, the random trisection approach[2]
randomly divides a closed disk centered at Si into three equal-sized sectors
and calculates di for a union of any two sectors. Now, NN(Si) denotes the
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Ren-Shiou Liu, Lifeng Sang, and Prasun Sinha
union yielding the largest |di| among the three. Again, the largest di will be
used instead of the old one to make the final decision.
Let C2 denote the set of sensors detected by the random bisection or
random trisection approach. Recall C1, the set of faulty sensors claimed by
the faulty sensor detection algorithm, may contain some sensors near the event
boundary as well. A better edge estimation technique is to find a set of sensors
C3 ?? C1 [ C2 excluding those C1 nodes without a C2 sensor nearby. Based
on the observation that sensor readings are spatially correlated, for a sensor
Si 2 C1 [ C2, we can draw a closed disk D(Si; c) with radius c centered at
Si. Since the majority of C2 sensors sit near the event boundary, if the closed
disk D(Si; c) contains at least one sensor node from C2, Si is expected to be
an edge sensor.
Thus, to determine C3 sensors, we have to decide an appropriate radius
c first. Since the density of the sensor field heavily e?®ects the accuracy of
boundary estimation, it is more desirable to control the number of expected
sensor nodes in the closed disk instead of the radius.
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