article

Incremental topological flipping works for regular triangulations

Authors:

H. Edelsbrunner,

N. R. ShahAuthors Info & Claims

Algorithmica, Volume 15, Issue 3

Pages 223 - 241

https://doi.org/10.1007/BF01975867

Published: 01 March 1996 Publication History

Abstract

A set ofn weighted points in general position in źd defines a unique regular triangulation. This paper proves that if the points are added one by one, then flipping in a topological order will succeed in constructing this triangulation. If, in addition, the points are added in a random sequence and the history of the flips is used for locating the next point, then the algorithm takes expected time at mostO(nlogn+n[d/2]). Under the assumption that the points and weights are independently and identically distributed, the expected running time is between proportional to and a factor logn more than the expected size of the regular triangulation. The expectation is over choosing the points and over independent coin-flips performed by the algorithm.

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Index Terms

Incremental topological flipping works for regular triangulations
1. Mathematics of computing
  1. Discrete mathematics
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Algorithmica

Algorithmica Volume 15, Issue 3

March 1996

82 pages

ISSN:0178-4617

Issue’s Table of Contents

Copyright © Copyright © 1996 Springer-Verlag New York Inc.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 1996

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Cited By

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https://dl.acm.org/doi/10.1145/3626246.3654691
Pan JWang JLi G(2024)Survey of vector database management systemsThe VLDB Journal — The International Journal on Very Large Data Bases10.1007/s00778-024-00864-x33:5(1591-1615)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s00778-024-00864-x
Cohen-Steiner DLieutier AVuillamy J(2023)Delaunay and Regular Triangulations as Lexicographic Optimal ChainsDiscrete & Computational Geometry10.1007/s00454-023-00485-170:1(1-50)Online publication date: 16-May-2023
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Si H(2015)TetGen, a Delaunay-Based Quality Tetrahedral Mesh GeneratorACM Transactions on Mathematical Software10.1145/262969741:2(1-36)Online publication date: 4-Feb-2015
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Silva LScheidegger LEtiene TComba JNonato LSilva C(2014)A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious FashionComputer Graphics Forum10.1111/cgf.1227433:6(18-30)Online publication date: 1-Sep-2014
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