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  Reliable and Efficient Computational Geometry Via Controlled Perturbation

Mehlhorn, K., Osbild, R., & Sagraloff, M. (2006). Reliable and Efficient Computational Geometry Via Controlled Perturbation. In Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I (pp. 299-310). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-23D5-3 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-23D7-0
Genre: Conference Paper

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 Creators:
Mehlhorn, Kurt1, Author           
Osbild, Ralf1, Author           
Sagraloff, Michael1, Author           
Bugliesi, Michele, Editor
Preneel, Bart, Editor
Sassone, Vladimir, Editor
Wegener, Ingo, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate input. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic may fail. Controlled perturbation replaces an input x by a random nearby in the δ-neighborhood of x and then runs the floating point version of the idealistic algorithm on . The hope is that this will produce the correct result for with constant probability provided that δ is small and the precision L of the floating point system is large enough. We turn this hope into a theorem for a large class of geometric algorithms and describe a general methodology for deriving a relation between δ and L. We exemplify the usefulness of the methodology by examples. Partially supported by the IST Programme of the EU under Contract No IST-006413, Algorithms for Complex Shapes (ACS).

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Language(s): eng - English
 Dates: 2007-03-282006
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 314533
Other: Local-ID: C1256428004B93B8-1C44F76383A124E7C12571CA003ABB0D-MOS06
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Title: Untitled Event
Place of Event: Venice, Italy
Start-/End Date: 2006-07-10

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Title: Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 299 - 310 Identifier: ISBN: 3-540-35904-4

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 4051 Sequence Number: - Start / End Page: - Identifier: -