Using the distribution of cells by dimension in a cylindrical algebraic decomposition

D. Wilson, M England, R.J. Bradford, J.H. Davenport

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

  • 6 Citations

Abstract

We investigate the distribution of cells by dimension in cylindrical algebraic decompositions (CADs). We find that they follow a standard distribution which seems largely independent of the underlying problem or CAD algorithm used. Rather, the distribution is inherent to the cylindrical structure and determined mostly by the number of variables.

This insight is then combined with an algorithm that produces only full-dimensional cells to give an accurate method of predicting the number of cells in a complete CAD. Since constructing only full-dimensional cells is relatively inexpensive (involving no costly algebraic number calculations) this leads to heuristics for helping with various questions of problem formulation for CAD, such as choosing an optimal variable ordering. Our experiments demonstrate that this approach can be highly effective.
LanguageEnglish
Title of host publicationSymbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on
PublisherIEEE
Pages53-60
Number of pages8
ISBN (Print)978-1-4799-8447-3
DOIs
StatusPublished - 2014

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Decompose
Cell
Algebraic number
Decomposition Algorithm
Heuristics
Formulation
Demonstrate
Experiment
Standards

Keywords

  • Cylindrical Algebraic Decomposition
  • problem formulation
  • heuristic

Cite this

Wilson, D., England, M., Bradford, R. J., & Davenport, J. H. (2014). Using the distribution of cells by dimension in a cylindrical algebraic decomposition. In Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on (pp. 53-60). IEEE. https://doi.org/10.1109/SYNASC.2014.15

Using the distribution of cells by dimension in a cylindrical algebraic decomposition. / Wilson, D.; England, M; Bradford, R.J.; Davenport, J.H.

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on. IEEE, 2014. p. 53-60.

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

Wilson, D, England, M, Bradford, RJ & Davenport, JH 2014, Using the distribution of cells by dimension in a cylindrical algebraic decomposition. in Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on. IEEE, pp. 53-60. https://doi.org/10.1109/SYNASC.2014.15
Wilson D, England M, Bradford RJ, Davenport JH. Using the distribution of cells by dimension in a cylindrical algebraic decomposition. In Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on. IEEE. 2014. p. 53-60 https://doi.org/10.1109/SYNASC.2014.15
Wilson, D. ; England, M ; Bradford, R.J. ; Davenport, J.H. / Using the distribution of cells by dimension in a cylindrical algebraic decomposition. Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on. IEEE, 2014. pp. 53-60
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