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On geometric optimization with few violated constraints
 J. Matoušek
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We investigate the problem of finding the best solution satisfying all butk of the given constraints, for an abstract class of optimization problems introduced by Sharir and Welzl—the socalledLPtype problems. We give a general algorithm and discuss its efficient implementations for specific geometric problems. For instance for the problem of computing the smallest circle enclosing all butk of the givenn points in the plane, we obtain anO(n logn+k ^{3} n ^{ε}) algorithm; this improves previous results fork small compared withn but moderately growing. We also establish some results concerning general properties ofLPtype problems.
This research was supported in part by Charles University Grant No. 351 and Czech Republic Grant GAČR 201/93/2167. Part of this research was performed while the author was visting the Computer Science Institute, Free University Berlin, and it was supported by the GermanIsraeli Foundation of Scientific Research and Development (G.I.F.), and part while visiting the MaxPlanck Institute for Computer Science in Saarbrücken.
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 Title
 On geometric optimization with few violated constraints
 Journal

Discrete & Computational Geometry
Volume 14, Issue 1 , pp 365384
 Cover Date
 19951201
 DOI
 10.1007/BF02570713
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 J. Matoušek ^{(1)}
 Author Affiliations

 1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 11800, Praha 1, Czech Republic