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

Fingerprint

Exact Computation
Exact Geometric Computation
Subdivision
Geometric Constraints
Zero set
Robust Algorithm
Zero
Path Planning
Numerical Algorithms
Pathway
Correctness
Computational Complexity
Motion planning
Robot
Computational complexity
Computing
Robots
Framework

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

Towards Soft Exact Computation (Invited Talk). / Yap, Chee.

Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. ed. / Evgenii V. Vorozhtsov; Timur M. Sadykov; Werner M. Seiler; Wolfram Koepf; Matthew England. Springer-Verlag, 2019. p. 12-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11661 LNCS).

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

Yap, C 2019, Towards Soft Exact Computation (Invited Talk). in EV Vorozhtsov, TM Sadykov, WM Seiler, W Koepf & M England (eds), Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11661 LNCS, Springer-Verlag, pp. 12-36, 21st International Workshop on Computer Algebra in Scientific Computing, CASC 2019, Moscow, Russian Federation, 8/26/19. https://doi.org/10.1007/978-3-030-26831-2_2
Yap C. Towards Soft Exact Computation (Invited Talk). In Vorozhtsov EV, Sadykov TM, Seiler WM, Koepf W, England M, editors, Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. Springer-Verlag. 2019. p. 12-36. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-26831-2_2
Yap, Chee. / Towards Soft Exact Computation (Invited Talk). Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings. editor / Evgenii V. Vorozhtsov ; Timur M. Sadykov ; Werner M. Seiler ; Wolfram Koepf ; Matthew England. Springer-Verlag, 2019. pp. 12-36 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{077b9f1f38f4472a895130321242aac3,
title = "Towards Soft Exact Computation (Invited Talk)",
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.",
author = "Chee Yap",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/978-3-030-26831-2_2",
language = "English (US)",
isbn = "9783030268305",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer-Verlag",
pages = "12--36",
editor = "Vorozhtsov, {Evgenii V.} and Sadykov, {Timur M.} and Seiler, {Werner M.} and Wolfram Koepf and Matthew England",
booktitle = "Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings",

}

TY - GEN

T1 - Towards Soft Exact Computation (Invited Talk)

AU - Yap, Chee

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85071445752&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85071445752&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-26831-2_2

DO - 10.1007/978-3-030-26831-2_2

M3 - Conference contribution

AN - SCOPUS:85071445752

SN - 9783030268305

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 12

EP - 36

BT - Computer Algebra in Scientific Computing - 21st International Workshop, CASC 2019, Proceedings

A2 - Vorozhtsov, Evgenii V.

A2 - Sadykov, Timur M.

A2 - Seiler, Werner M.

A2 - Koepf, Wolfram

A2 - England, Matthew

PB - Springer-Verlag

ER -