Consider a set of n sensors deployed in a “belt region” – that is, a rectangular
ID: 3841177 • Letter: C
Question
Consider a set of n sensors deployed in a “belt region” – that is, a rectangular region R that is aligned with the x-y axes, where typically the width along the x-axis is much larger than the height along the y-axis. Assume that each sensor has a sensing range of r. That is, the sensor can detect movement anywhere in or on the circle of radius r centered at the sensor. This set of sensors provides k-weak barrier coverage for R if an intruder moving across R on any path parallel to the y axis will be detected by at least k sensors. Here is an example where the sensors provide 1-weak barrier coverage:
Give an O(n log n) algorithm to determine if a set of n sensors provides k-weak barrier coverage for R.
An illustration of weak 1.barrier caverage: any orthogonal crossing path (dashed lines)is covered by at least one sensor, However, uncovered path(s) may exist, such as the anes shawn in the solid curves.Explanation / Answer
//starting point of the algorithm
Compute the k-weak barrier coverage
// Applying the data variable for three types
Data: solidCurves, straightLine, dashedLines
Result: solidCurves
weakBarrierSensor
weakBarrierSolidC = 1;
weakBarRS solidCurves;
Update weakCoverageNC;
Apply WBC to weakCoverageNC;
//while loop
while NCK != 0 do
weakBarrierSolidC weakBarrierSolidC + 1;
Update weakBarRSOne and weakCoverageNCs;
Apply WBC to weakCoverageNCs;
//end of the algorithm
end