Smallest-circle problem: Difference between revisions

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The minimum covering circle problem is a mathematical problem of computing a smallest enclosing circle of a set S of given N points in Rⁿ, which was initially proposed by Sylvester in 1987. This problem is also called minimum covering circle problem. In two dimensional space, the problem is a well known single facility location problem which locates a new facility to provide service to a number of customers or facilities. We can formulate the minimum covering circle problem as the minimax programming problem:

$\min _{x\in R^{n}}\max _{x\in S}\|x-s\|$

The problem can be reduced to the following minimization problem:

$\min r$ with subject to $\|x-s\|\leq r$

References

External links

Bernd Gärtner's smallest enclosing ball code
Miniball open source project for smallest enclosing balls

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 The '''minimum covering circle problem''' is a [[mathematical problem]] of computing a smallest enclosing circle of a set S of given N points in R<sup>n</sup>, which was initially proposed by Sylvester in 1987. This problem is also called minimum covering circle problem. In two dimensional space, the problem is a well known single facility location problem which locates a new facility to provide service to a number of customers or facilities. We can formulate the minimum covering circle problem as the minimax programming problem:
-<math> min_{x\in R^n} max_{x\in S} \|x-s\|</math>
+<math> \min_{x\in R^n} \max_{x\in S} \|x-s\|</math>
+The problem can be reduced to the following minimization problem:
+<math>\min r</math>
+with subject to
+<math>\|x-s\|\leq r</math>
 ==References==
 {{reflist}}