## Backwards Analysis of Randomized Geometric Algorithms (1992)

Venue: | Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics |

Citations: | 58 - 0 self |

### BibTeX

@INPROCEEDINGS{Seidel92backwardsanalysis,

author = {Raimund Seidel},

title = {Backwards Analysis of Randomized Geometric Algorithms},

booktitle = {Trends in Discrete and Computational Geometry, volume 10 of Algorithms and Combinatorics},

year = {1992},

pages = {37--68},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

The theme of this paper 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. 1 Introduction The curious phenomenon that randomness can be used profitably in the solution of computational tasks has attracted a lot of attention from researchers in recent years. The approach has proved useful in such diverse area...

### Citations

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Citation Context ...rties by Shamos and Hoey [53] were instrumental in getting the field of computational geometry started. By now these structures along with numerous generalizations are standard fare in the field (see =-=[45, 25, 3, 36]-=-). Shamos's and Hoey's big feat was an O(n log n) algorithm for the construction of Delaunay triangulations. It was also very soon realized that the O(n log n) bound was asymptotically worst case opti... |

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Citation Context ...rties by Shamos and Hoey [53] were instrumental in getting the field of computational geometry started. By now these structures along with numerous generalizations are standard fare in the field (see =-=[45, 25, 3, 36]-=-). Shamos's and Hoey's big feat was an O(n log n) algorithm for the construction of Delaunay triangulations. It was also very soon realized that the O(n log n) bound was asymptotically worst case opti... |

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Citation Context ...vestigator Award CCR-9058440. Email address: seidel@cs.berkeley.edu the Euclidean closest pair problem. Of course computational geometry as a field came about a number of years later. Shamos's thesis =-=[52] appeared in 19-=-78. Talking about possible future research directions in the epilogue Shamos mentions "probabilistic algorithms" and writes "This approach seems to be able to yield geometric algorithms... |

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Citation Context ...constant time, say, the leftmost face of G S (R 0 ) that is intersected by s. Now we "thread" s through G S (R 0 ) in the usual way, similar to the incremental line arrangement construction =-=algorithm [27, 13]-=-: We walk along the segment s; assume we just entered a face f through some edge e; we determine through which edge the segment s leaves f and which new face the segment enters by simply testing all e... |

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Concrete and Abstract Voronoi diagrams
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Citation Context ...multiplicative factor of c is only O(n \Gammac(log c\Gamma1) ). 5 Backwards Analysis of QUICKSORT QUICKSORT constitutes the archetypical example of a randomized 2 algorithm. Invented by Hoare in 1960 =-=[33]-=-, it has since been amply analyzed (see for instance Sedgewick's book [49]) and with its various versions it has become the maybe most frequently used sorting algorithm in practice. We will consider a... |

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19 |
Reporting and counting segment intersections
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6 |
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3 |
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3 |
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