Discrete & Computational Geometry

, Volume 14, Issue 4, pp 365–384

On geometric optimization with few violated constraints

  • J. Matoušek

DOI: 10.1007/BF02570713

Cite this article as:
Matoušek, J. Discrete & Computational Geometry (1995) 14: 365. doi:10.1007/BF02570713


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 so-calledLP-type 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+k3nε) algorithm; this improves previous results fork small compared withn but moderately growing. We also establish some results concerning general properties ofLP-type problems.

Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • J. Matoušek
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPraha 1Czech Republic