Abstract
AbstractWhen the input polynomial set has a chordal associated graph, top-down algorithms for triangular decomposition are proved to preserve the chordal structure. Based on these theoretical results, sparse algorithms for triangular decomposition were proposed and demonstrated with experiments to be more efficient in case of sparse polynomial sets. However, existing implementations of top-down triangular decomposition are not guaranteed to be chordality-preserving due to operations which potentially destroy the chordality. In this paper, we first analyze the current implementations of typical top-down algorithms for triangular decomposition in the Epsilon package to identify these chordality-destroying operations. Then modifications are made accordingly to guarantee new implementations of such algorithms are chordality-preserving. In particular, the technique of dynamic checking is introduced to ensure that the modifications also keep the computational efficiency. Experimental results with polynomial sets from biological systems are also reported.KeywordsTriangular decompositionChordal graphSparsityImplementation
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
