Applications of random sampling in computational geometry, II

@inproceedings{Clarkson1988ApplicationsOR,
  title={Applications of random sampling in computational geometry, II},
  author={Kenneth L. Clarkson},
  booktitle={SCG '88},
  year={1988}
}
  • K. Clarkson
  • Published in SCG '88 6 January 1988
  • Mathematics, Computer Science
Random sampling is used for several new geometric algorithms. The algorithms are “Las Vegas,” and their expected bounds are with respect to the random behavior of the algorithms. One algorithm reports all the intersecting pairs of a set of line segments in the plane, and requires <italic>&Ogr;</italic>(<italic>A</italic> + <italic>n</italic> log <italic>n</italic>) expected time, where <italic>A</italic> is the size of the answer, the number of intersecting pairs reported. The algorithm… 
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This paper presents a deterministic algorithm which is faster than Matousk's recent algorithm [Ma] for large values of r, and applies it to several problems involving lines or segments in the plane, and obtain deterministic algorithms which are faster than any previously known algorithms.
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