Removing Degeneracies by Perturbing the Problem or Perturbing the World

Removing Degeneracies by Perturbing the Problem or Perturbing the World We describe two problem-specific approaches to remove geometric degeneracies that we call perturbing the problem and perturbing the world. Using as our primary examples 2-d and 3-d Delaunay triangulation with Euclidean and polygonal metrics, we show that these approaches lead to relatively simple and efficient perturbations of the points that do not depend on a fixed ordering or index. Thus, they produce canonical output, which is important for producing test suites and verifiers for randomized or dynamic geometric algorithms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Removing Degeneracies by Perturbing the Problem or Perturbing the World

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2000 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009942427413
Publisher site
See Article on Publisher Site

Abstract

We describe two problem-specific approaches to remove geometric degeneracies that we call perturbing the problem and perturbing the world. Using as our primary examples 2-d and 3-d Delaunay triangulation with Euclidean and polygonal metrics, we show that these approaches lead to relatively simple and efficient perturbations of the points that do not depend on a fixed ordering or index. Thus, they produce canonical output, which is important for producing test suites and verifiers for randomized or dynamic geometric algorithms.

Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

References

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