Given $\cA := \{a^1,\ldots,a^m\} \subset \R^n$, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of $\cA$. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in $\cA$ that are guaranteed to lie in the interior of the minimum-radius ball enclosing $\cA$. Our computational results reveal that incorporating this procedure into the two recent algorithms proposed by \Yildirim~leads to significant speed-ups in running times especially for randomly generated large-scale problems. We also illustrate that the extra overhead due to the elimination procedure remains at an acceptable level for spherical or almost spherical input sets.

## Citation

SIAM J. Optim. Volume 19, Issue 3, pp. 1392-1396 (2008)

## Article

View Identification and Elimination of Interior Points for the Minimum Enclosing Ball Problem