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New Trends in Discrete and Computational Geometry pp 37–67Cite as

Backwards Analysis of Randomized Geometric Algorithms

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Part of the book series: Algorithms and Combinatorics ((AC,volume 10))

Abstract

The theme of this chapter is a rather simple method that has proved very potent in the analysis of the expected performance of various randomized algorithms and data structures in computational geometry. The method can be described as “analyze a randomized algorithm as if it were running backwards in time, from output to input.” We apply this type of analysis to a variety of algorithms, old and new, and obtain solutions with optimal or near optimal expected performance for a plethora of problems in computational geometry, such as computing Delaunay triangulations of convex polygons, computing convex hulls of point sets in the plane or in higher dimensions, sorting, intersecting line segments, linear programming with a fixed number of variables, and others.

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Authors
  1. Raimund Seidel
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Editors and Affiliations

  1. Mathematical Institute of the Hungarian Academy of Sciences, H-1364, Budapest, PF-127, Hungary

    János Pach

  2. Courant Institute, New York University, 251 Mercer Street, New York, NY, 10012, USA

    János Pach

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© 1993 Springer-Verlag Berlin Heidelberg

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Seidel, R. (1993). Backwards Analysis of Randomized Geometric Algorithms. In: Pach, J. (eds) New Trends in Discrete and Computational Geometry. Algorithms and Combinatorics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58043-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-58043-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55713-5

  • Online ISBN: 978-3-642-58043-7

  • eBook Packages: Springer Book Archive

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