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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