Applications of parametric searching in geometric optimization
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
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\indent Given a set $S$ of $n$ points in the plane and a segment $e$, a {\em center placement} of $e$ is a placement (allowing translation and rotation) that minimizes the maximum distance from $e$ to the points of $S$. We present an algorithm for computing a center placement for $S$, whose running time is $O(n^{2} \alpha (n) \, \mbox {log} ^{3}n),$ where $\alpha (n)$ is the inverse Ackermann function. The algorithm makes use of the parametric searching technique of Megiddo.