Günter Rote, Christian Schwarz, and Jack Snoeyink:

Maintaining the approximate width of a set of points in the plane (extended abstract)

In: Proceedings of the Fifth Canadian Conference on Computational Geometry, Waterloo, August 5-9, 1993. Editor: A. Lubiw, J. Urrutia; pp. 258-263.

Abstract

The width of a set of n points in the plane is the smallest distance between two parallel lines that enclose the set. We maintain the set of points under insertions and deletions of points and we are able to report an approximation of the width of this dynamic point set. Our data structure takes linear space and allows for reporting the approximation with relative accuracy epsilon in O(sqrt(1/epsilon) log n) time; and the update time is O(log2 n). The method uses the tentative prune-and-search strategy of Kirkpatrick and Snoeyink
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