Towards Soft Exact Computation (Invited Talk)

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Exact geometric computation (EGC) is a general approach for achieving robust numerical algorithms that satisfy geometric constraints. At the heart of EGC are various Zero Problems, some of which are not-known to be decidable and others have high computational complexity. Our current goal is to introduce notions of “soft- correctness” in order to avoid Zero Problems. We give a bird’s eye view of our recent work with collaborators in two principle areas: computing zero sets and robot path planning. They share a common Subdivision Framework. Such algorithms (a) have adaptive complexity, (b) are practical, and (c) are effective. Here, “effective algorithm” means it is easily and correctly implementable from standardized algorithmic components. Our goals are to outline these components and to suggest new components to be developed. We discuss a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework.

Original languageEnglish (US)
Title of host publicationComputer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings
EditorsEvgenii V. Vorozhtsov, Timur M. Sadykov, Werner M. Seiler, Wolfram Koepf, Matthew England
PublisherSpringer-Verlag
Pages12-36
Number of pages25
ISBN (Print)9783030268305
DOIs
StatePublished - Jan 1 2019
Event21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019 - Moscow, Russian Federation
Duration: Aug 26 2019Aug 30 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11661 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019
CountryRussian Federation
CityMoscow
Period8/26/198/30/19

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yap, C. (2019). Towards Soft Exact Computation (Invited Talk). In E. V. Vorozhtsov, T. M. Sadykov, W. M. Seiler, W. Koepf, & M. England (Eds.), Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings (pp. 12-36). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11661 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-26831-2_2