Approximate Shape fitting via Linearization

Sariel Har-Peled and Kasturi R. Varadarajan

Shape fitting is a fundamental optimization problem in computer science. In this paper, we present a general and unified technique for solving a certain family of such problems. Given a point set P in R^d, this technique can be used to µ-approximate:(i) the min-width annulus and shell that contains P,(ii) minimum width cylindrical shell containing P,(iii) diameter, width, minimum volume bounding box of P, and(iv) all the previous measures for the case the points are moving. The running time of the resulting algorithms is O(n + 1/µ^c), where c is a constant that depends on the problem at hand.

Our new general technique enable us to solve those problems without resorting to a careful and painful case by case analysis, as was previously done for those problems. Furthermore, for several of those problems our results are considerably simpler and faster than what was previously known. In particular, for the minimum width cylindrical shell problem, our solution is the first algorithm whose running time is subquadratic in n.(In fact we get running time linear in n.)

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@string{FOCS_2001 = "Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci."}
@inproceedings{hv-asfl-01,
   author =       {S.~{Har-Peled} and K.R.~Varadarajan},
   title =        {Approximate Shape Fitting via Linearization},
   booktitle =    FOCS_2001,
   year =         2001,
   pages = "66--73"
}

Last updated: Mon Mar 19 10:54:18 CST 2001