Cargando…
Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks
Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heuristic ones on selecting the best variable ordering when the number of variables [Formula: s...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2020
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340889/ http://dx.doi.org/10.1007/978-3-030-52200-1_28 |
_version_ | 1783555114923982848 |
---|---|
author | Chen, Changbo Zhu, Zhangpeng Chi, Haoyu |
author_facet | Chen, Changbo Zhu, Zhangpeng Chi, Haoyu |
author_sort | Chen, Changbo |
collection | PubMed |
description | Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heuristic ones on selecting the best variable ordering when the number of variables [Formula: see text]. One main challenge for handling the general case is the exponential explosion of number of different orderings when n increases. In this paper, we propose an iterative method for generating candidate variable orderings and an ML approach for selecting the best ordering from them via learning neural network classifiers. Experimentations show that this approach outperforms heuristic ones for [Formula: see text]. |
format | Online Article Text |
id | pubmed-7340889 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-73408892020-07-08 Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks Chen, Changbo Zhu, Zhangpeng Chi, Haoyu Mathematical Software – ICMS 2020 Article Cylindrical algebraic decomposition (CAD) is a fundamental tool in computational real algebraic geometry. Previous studies have shown that machine learning (ML) based approaches may outperform traditional heuristic ones on selecting the best variable ordering when the number of variables [Formula: see text]. One main challenge for handling the general case is the exponential explosion of number of different orderings when n increases. In this paper, we propose an iterative method for generating candidate variable orderings and an ML approach for selecting the best ordering from them via learning neural network classifiers. Experimentations show that this approach outperforms heuristic ones for [Formula: see text]. 2020-06-06 /pmc/articles/PMC7340889/ http://dx.doi.org/10.1007/978-3-030-52200-1_28 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Chen, Changbo Zhu, Zhangpeng Chi, Haoyu Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title | Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title_full | Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title_fullStr | Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title_full_unstemmed | Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title_short | Variable Ordering Selection for Cylindrical Algebraic Decomposition with Artificial Neural Networks |
title_sort | variable ordering selection for cylindrical algebraic decomposition with artificial neural networks |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340889/ http://dx.doi.org/10.1007/978-3-030-52200-1_28 |
work_keys_str_mv | AT chenchangbo variableorderingselectionforcylindricalalgebraicdecompositionwithartificialneuralnetworks AT zhuzhangpeng variableorderingselectionforcylindricalalgebraicdecompositionwithartificialneuralnetworks AT chihaoyu variableorderingselectionforcylindricalalgebraicdecompositionwithartificialneuralnetworks |