Geometric applications of a randomized optimization technique

@inproceedings{Chan1998GeometricAO,
  title={Geometric applications of a randomized optimization technique},
  author={Timothy M. Chan},
  booktitle={SCG '98},
  year={1998}
}
We propose a simple, general, randomized technique to reduce certain geo- metric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra log- arithmic 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… Expand
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References

SHOWING 1-9 OF 9 REFERENCES
On geometric optimization with few violated constraints
  • J. Matousek
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1995
  • 94
  • Highly Influential
  • PDF
E cient Algorithms for Geometric Optimization
  • 12
  • Highly Influential
  • PDF
Optimal Slope Selection Via Expanders
  • 50
  • Highly Influential
k-Violation Linear Programming
  • 34
  • Highly Influential
Getting around a lower bound for the minimum Hausdorff distance
  • 23
  • Highly Influential
Linear time algorithms for linear program- ming in R3 and related problems
  • SIAM J. Comput.,
  • 1983
Iterated nearest neigh- bors and nding minimal polytopes
  • Discrete Comput. Geom.,
  • 1994
and M
  • van Kreveld. An optimal algorithm for the ( k)-levels, with applica- tions to separation and transversal problems. Int. J. Comput. Geom. Appl., 6:247{261
  • 1996
Approximate nearest neigh- bor queries in xed dimensions
  • In Proc. 4th ACM- SIAM Sympos. Discrete Algorithms,
  • 1993