Using the Distribution of Cells by Dimension in a Cylindrical Algebraic Decomposition

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 an...

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Bibliographic Details
Published in:2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 53 - 60
Main Authors: Wilson, David, England, Matthew, Bradford, Russell, Davenport, James H.
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2014
Subjects:
Buildings
cell distribution
Complexity theory
cylindrical algebraic decomposition
Design automation
heuristic
Polynomials
Prediction algorithms
problem formulation
Scientific computing
ISBN:9781479984473, 1479984477
Online Access:Get full text
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Summary: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.
ISBN:9781479984473
1479984477
DOI:10.1109/SYNASC.2014.15