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  • 1
    Electronic Resource
    Electronic Resource
    Finding extrema with unary predicates (1993)
    Springer
    Algorithmica 9 (1993), S. 591-600 
    Details
    ISSN: 1432-0541
    Keywords: Adversary argument ; Algorithms ; Communication complexity ; Lower bounds ; Maximum finding ; Threshold predicates ; Unary predicates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the problem of determining the maximum and minimum elements of a setX={x1...,x n }, drawn from some finite universeU of real numbers, using only unary predicates of the inputs. It is shown that θ(n+ log¦U¦) unary predicate evaluations are necessary and sufficient, in the worst case. Results are applied to (i) the problem of determining approximate extrema of a set of real numbers, in the same model, and (ii) the multiparty broadcast communication complexity of determining the extrema of an arbitrary set of numbers held by distinct processors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190157
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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