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  • Articles  (3)
  • divide-and-conquer  (2)
  • 52.A10  (1)
  • Springer  (3)
  • American Association of Petroleum Geologists (AAPG)
  • American Chemical Society
  • Blackwell Publishing Ltd
  • 1980-1984  (3)
  • 1945-1949
  • Computer Science  (3)
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  • Articles  (3)
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  • Springer  (3)
  • American Association of Petroleum Geologists (AAPG)
  • American Chemical Society
  • Blackwell Publishing Ltd
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  • 1
    Electronic Resource
    Electronic Resource
    Applications of a two-dimensional hidden-line algorithm to other geometric problems (1983)
    Springer
    Computing 31 (1983), S. 191-202 
    Details
    ISSN: 1436-5057
    Keywords: 52.A30 ; 52.A10 ; Visibility ; simple polygon ; convex hull ; triangulation ; L-convex polygon ; edge visible polygon ; geometric complexity ; algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Kürzlich haben ElGindy und Avis (EA) einenO(n)-Algorithmus zur Lösung des Problems der verdeckten Linien in einem überschneidungsfreien Polygon vorgelegt. Hier zeigen wir, daß ihr Algorithmus auch zur Lösung anderer geometrischer Probleme verwendet werden kann. Insbesondere können wir einL-konvexes Polygon in der ZeitO(n) triangulieren und die konvexe Hülle eines überschneidungsfreien Polygons in der gleichen Zeit finden. Ferner kann die Überprüfung eines überschneidungsfreien Polygons aufL-Konvexität in der ZeitO (n2) erfolgen.
    Notes: Abstract Recently ElGindy and Avis (EA) presented anO(n) algorithm for solving the two-dimensional hidden-line problem in ann-sided simple polygon. In this paper we show that their algorithm can be used to solve other geometric problems. In particular, triangulating anL-convex polygon and finding the convex hull of a simple polygon can be accomplished inO(n) time, whereas testing a simple polygon forL-convexity can be done inO(n 2) time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02263430
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An optimal time and minimal space algorithm for rectangle intersection problems (1984)
    Springer
    International journal of parallel programming 13 (1984), S. 23-32 
    Details
    ISSN: 1573-7640
    Keywords: Computational geometry ; analysis of algorithms ; rectangle intersection ; divide-and-conquer ; disjoint set union-find
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Given a set ofn iso-oriented rectangles in the plane whose sides are parallel to the coordinate axes, we consider the rectangle intersection problem, i.e., finding alls intersecting pairs. The problem is well solved in the past and its solution relies heavily on unconventional data structures such as range trees, segment trees or rectangle trees. In this paper we demonstrate that classical divide-and-conquer technique and conventional data structures such as linked lists are sufficient to achieve a time bound ofO(n logn) +s, and a space bound of Θ(n), both of which are optimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989481
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  • 3
    Electronic Resource
    Electronic Resource
    Two algorithms for constructing a Delaunay triangulation (1980)
    Springer
    International journal of parallel programming 9 (1980), S. 219-242 
    Details
    ISSN: 1573-7640
    Keywords: Delaunay triangulation ; triangulation ; divide-and-conquer ; Voronoi tessellation ; computational geometry ; analysis of algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed. Two algorithms are presented for constructing the triangulation over a planar set ofN points. The first algorithm uses a divide-and-conquer approach. It runs inO(N logN) time, which is asymptotically optimal. The second algorithm is iterative and requiresO(N 2) time in the worst case. However, its average case performance is comparable to that of the first algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00977785
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