A fast planar partition algorithm. I

@article{Mulmuley1988AFP,
  title={A fast planar partition algorithm. I},
  author={Ketan Mulmuley},
  journal={[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science},
  year={1988},
  pages={580-589}
}
  • K. Mulmuley
  • Published 24 October 1988
  • Mathematics, Computer Science
  • [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
A fast randomized algorithm is given for finding a partition of the plane induced by a given set of linear segments. The algorithm is ideally suited for a practical use because it is extremely simple and robust, as well as optimal; its expected running time is O(m+n log n) where n is the number of input segments and m is the number of points of intersection. The storage requirement is O(m+n). Though the algorithm itself is simple, the global evolution of the partition is complex, which makes… 
A Fast Planar Partition Algorithm, I
  • K. Mulmuley
  • Mathematics, Computer Science
    J. Symb. Comput.
  • 1990
TLDR
Though the algorithm itself is simple, the global evolution of the underlying partition is non-trivial, which makes the analysis of the algorithm theoretically interesting in its own right.
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  • J. Matousek
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  • 1989
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A new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations is given which obviates the need for building a separate point-location structure for nearest-neighbor queries.
Randomized incremental construction of Delaunay and Voronoi diagrams
TLDR
A new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations is given that takes expected timeO(nℝgn) and spaceO( n), and is eminently practical to implement.
Dynamic maintenance of geometric structures made easy
  • O. Schwarzkopf
  • Mathematics
    [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
  • 1991
The problem of dynamically maintaining geometric structures is considered. A technique is proposed that uses randomized incremental algorithms which are augmented to allow deletions of objects. A
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