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  • 1
    Electronic Resource
    Electronic Resource
    Visibility of disjoint polygons (1986)
    Springer
    Algorithmica 1 (1986), S. 49-63 
    Details
    ISSN: 1432-0541
    Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840436
    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
    A multiplicative barrier function method for linear programming (1986)
    Springer
    Algorithmica 1 (1986), S. 455-482 
    Details
    ISSN: 1432-0541
    Keywords: Linear programming ; Interior method ; Barrier function ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A simple Newton-like descent algorithm for linear programming is proposed together with results of preliminary computational experiments on small- and medium-size problems. The proposed algorithm gives local superlinear convergence to the optimum and, experimentally, shows global linear convergence. It is similar to Karmarkar's algorithm in that it is an interior feasible direction method and self-correcting, while it is quite different from Karmarkar's in that it gives superlinear convergence and that no artificial extra constraint is introduced nor is protective geometry needed, but only affine geometry suffices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840457
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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