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.
|Title of host publication||Proceedings - 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2014|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||8|
|Publication status||Published - 5 Feb 2015|
|Event||16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania|
Duration: 22 Sep 2014 → 25 Sep 2014
Conference number: 16
|Conference||16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing|
|Abbreviated title||SYNASC 2014|
|Period||22/09/14 → 25/09/14|
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- cell distribution
- cylindrical algebraic decomposition
- problem formulation
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Theoretical Computer Science
- Applied Mathematics