Discrete & Computational Geometry

, Volume 22, Issue 4, pp 547–567 | Cite as

Geometric Applications of a Randomized Optimization Technique

  • T. M. Chan


We propose a simple, general, randomized technique to reduce certain geometric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra logarithmic factors in previous, often more complicated, deterministic approaches (such as parametric searching). Faster algorithms are thus obtained for a variety of problems in computational geometry: finding minimal k -point subsets, matching point sets under translation, computing rectilinear p -centers and discrete 1-centers, and solving linear programs with k violations.


Time Complexity Optimization Technique Decision Problem Constant Factor Fast Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • T. M. Chan
    • 1
  1. 1.Current address: Department of Computer Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

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