Abstract
We speed up previous ( 1 + ε ) -factor approximation algorithms for a number of geometric optimization problems in fixed dimensions: diameter, width, minimum-radius enclosing cylinder, minimum-width enclosing annulus, minimum-width enclosing cylindrical shell, etc. Linear time bounds were known before; we further improve the dependence of the “constants” in terms of ε. We next consider the data-stream model and present new ( 1 + ε ) -factor approximation algorithms that need only constant space for all of the above problems in any fixed dimension. Previously, such a result was known only for diameter. Both sets of results are obtained using the core-set framework recently proposed by Agarwal, Har-Peled, and Varadarajan.
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