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  • Deterministic and randomized algorithms  (1)
  • Duality  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Algorithms for bichromatic line-segment problems and polyhedral terrains (1994)
    Springer
    Algorithmica 11 (1994), S. 116-132 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Line-segment intersection ; Segment trees ; Lines in space ; Polyhedral terrains ; Deterministic and randomized algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider a variety of problems on the interaction between two sets of line segments in two and three dimensions. These problems range from counting the number of intersecting pairs between m blue segments andn red segments in the plane (assuming that two line segments are disjoint if they have the same color) to finding the smallest vertical distance between two nonintersecting polyhedral terrains in three-dimensional space. We solve these problems efficiently by using a variant of the segment tree. For the three-dimensional problems we also apply a variety of recent combinatorial and algorithmic techniques involving arrangements of lines in three-dimensional space, as developed in a companion paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182771
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Planar geometric location problems (1994)
    Springer
    Algorithmica 11 (1994), S. 185-195 
    Details
    ISSN: 1432-0541
    Keywords: Facility location ; Parametric searching ; Duality ; Planar arrangements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present anO(n 2 log3 n) algorithm for the two-center problem, in which we are given a setS ofn points in the plane and wish to find two closed disks whose union containsS so that the larger of the two radii is as small as possible. We also give anO(n 2 log5 n) algorithm for solving the two-line-center problem, where we want to find two strips that coverS whose maximum width is as small as possible. The best previous solutions of both problems requireO(n 3) time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182774
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    Paper (German National Licenses)
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