# circles required to cover the perimeter of rectangle

Suppose sensor nodes of homogeneous sensing ranges are dropped by Poisson distribution around the given rectangle of area l*h. How do i calculate the minimum number of circles required to cover the perimeter of rectangle so that probability of coverage is greater than 90 percent

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I doubt an exact calculation is feasible. However, if the rectangle is large, then you should be able to get a good approximation by breaking the perimeter up into pieces, most of which are covered roughly independently and with probability close to $1$. Then use inclusion-exclusion. –  Douglas Zare May 21 '13 at 8:23