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- W2962928298 abstract "In this paper the chordal graph structures of polynomial sets appearing in triangular decomposition in top-down style are studied when the input polynomial set to decompose has a chordal associated graph. In particular, we prove that the associated graph of one specific triangular set computed in any algorithm for triangular decomposition in top-down style is a subgraph of the chordal graph of the input polynomial set and that all the polynomial sets including all the computed triangular sets appearing in one specific simply-structured algorithm for triangular decomposition in top-down style (Wang's method) have associated graphs which are subgraphs of the the chordal graph of the input polynomial set. These subgraph structures in triangular decomposition in top-down style are multivariate generalization of existing results for Gaussian elimination and may lead to specialized efficient algorithms and refined complexity analyses for triangular decomposition of chordal polynomial sets." @default.
- W2962928298 created "2019-07-30" @default.
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- W2962928298 date "2018-07-11" @default.
- W2962928298 modified "2023-10-17" @default.
- W2962928298 title "On the Chordality of Polynomial Sets in Triangular Decomposition in Top-Down Style" @default.
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- W2962928298 doi "https://doi.org/10.1145/3208976.3208997" @default.
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