Observations on the Minimum Sphere Problem.
FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING
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For a subset A of Euclidean n-space, the location problem of finding the point x which minimizes the maximum distance dx, a for a in A may be interpreted as finding the smallest sphere which encloses A. Algorithms have previously been developed for the situations when A is finite or a polytope. Here we concentrate on interpretations and properties of the problem, particularly its relation to other problems cases where the sphere problem is dual to that of finding a shortest vector in A, where there is a connection with a maximum moment-of-inertia problem, etc. Conjectures, relating the minimum sphere to points in A which define the diameter of A, are also discussed. Author
- Theoretical Mathematics