Smallest Enclosing Disks (balls and Ellipsoids) (1991) [123 citations — 2 self]
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author = {Emo Welzl},
title = {Smallest Enclosing Disks (balls and Ellipsoids)},
booktitle = {Results and New Trends in Computer Science},
year = {1991},
pages = {359--370},
publisher = {Springer-Verlag}
}
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Abstract:
A simple randomized algorithm is developed which computes the smallest enclosing disk of a finite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids of point sets in higher dimensions in a straightforward way. Experimental results of an implementation are presented. 1 Introduction During the recent years randomized algorithms have been developed for a host of problems in computational geometry. Many of these algorithms are not only attractive because of their efficiency, but also because of their appealing simplicity. This feature makes them easier to access for non-experts in the field, and for actual implementation. One of these simple algorithms is Seidel's Linear Programming algorithm, [Sei1], which solves a Linear Program with n constraints and d variables in expected O(n) time, provided d is constant
