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I have a question.The question is this.

Say you have a finite set S of n points in a circular disc. Think of the points in S as houses on a circular island. You want to locate a garbage incineration plant on the island, but of course as far away from each house as possible. How would you find the optimal placement for the plant? In other words, how would you identify a point in the disc that is as far away from each point of S as possible. Identify a set L of O(n) locations, one of which must be the optimal one

So with my researches I find these links as kind of answer.

standard raster solution

Detailed raster solution

But my problem is I did not really understand what should I use. Should I identify a random point,than check the distance of it with each point and sum them.I can do it many times,but I belive I can never be sure about if it is the farthest point to that set of points. As far as I understand from question,I can get unlimited number of points.

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  • $\begingroup$ So, given a disc $D$ and points $z_1,\dots, z_n$ in $D$ you wish to find a point $z\in D$ such that the minimum distance $\min \{|z-z_i|:i=1,\dots,n\}$ from $z$ to $z_i$ is as big as possible, right? $\endgroup$
    – Alex Ravsky
    Commented Jan 30, 2019 at 21:38
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    $\begingroup$ @AlexRavsky yes. My new point should be on the disk and also as far as I got it it should be far away from each point of that set $\endgroup$
    – yahya emre
    Commented Jan 31, 2019 at 0:14

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