Detecting all dependences in systems of geometric constraints using the witness method

Dominique Michelucci, Sebti Foufou

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

Abstract

In geometric constraints solving, the detection of dependences and the decomposition of the system into smaller subsystems are two important steps that characterize any solving process, but nowadays solvers, which are graph-based in most of the cases, fail to detect dependences due to geometric theorems and to decompose such systems. In this paper, we discuss why detecting all dependences between constraints is a hard problem and propose to use the witness method published recently to detect both structural and non structural dependences. We study various examples of constraints systems and show the promising results of the witness method in subtle dependences detection and systems decomposition.

Original languageEnglish (US)
Title of host publicationAutomated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers
Pages98-112
Number of pages15
StatePublished - Dec 1 2007
Event6th International Workshop on Automated Deduction in Geometry, ADG 2006 - Pontevedra, Spain
Duration: Aug 31 2006Sep 2 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4869 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Workshop on Automated Deduction in Geometry, ADG 2006
CountrySpain
CityPontevedra
Period8/31/069/2/06

Fingerprint

Geometric Constraints
Decomposition
Decompose
Geometric Constraint Solving
Geometric theorem
Subsystem
Graph in graph theory

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Michelucci, D., & Foufou, S. (2007). Detecting all dependences in systems of geometric constraints using the witness method. In Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers (pp. 98-112). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4869 LNAI).

Detecting all dependences in systems of geometric constraints using the witness method. / Michelucci, Dominique; Foufou, Sebti.

Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. p. 98-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4869 LNAI).

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

Michelucci, D & Foufou, S 2007, Detecting all dependences in systems of geometric constraints using the witness method. in Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4869 LNAI, pp. 98-112, 6th International Workshop on Automated Deduction in Geometry, ADG 2006, Pontevedra, Spain, 8/31/06.
Michelucci D, Foufou S. Detecting all dependences in systems of geometric constraints using the witness method. In Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. p. 98-112. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Michelucci, Dominique ; Foufou, Sebti. / Detecting all dependences in systems of geometric constraints using the witness method. Automated Deduction in Geometry - 6th International Workshop, ADG 2006, Revised Papers. 2007. pp. 98-112 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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