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On the Chordality of Simple Decomposition in Top-Down Style

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Mathematical Aspects of Computer and Information Sciences (MACIS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11989))

Abstract

Simple decomposition of polynomial sets computes conditionally squarefree triangular sets or systems with certain zero or ideal relationships with the polynomial sets. In this paper we study the chordality of polynomial sets occurring in the process of simple decomposition in top-down style. We first reformulate Wang’s algorithm for simple decomposition in top-down style so that the decomposition process can be described in an inductive way. Then we prove that for a polynomial set whose associated graph is chordal, all the polynomial sets in the process of Wang’s algorithm for computing simple decomposition of this polynomial set have associated graphs which are subgraphs of the input chordal graph.

This work was partially supported by the National Natural Science Foundation of China (NSFC 11971050 and 11771034) and the Fundamental Research Funds for the Central Universities in China (YWF-19-BJ-J-324).

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Authors and Affiliations

  1. LMIB–School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Chenqi Mou & Jiahua Lai

  2. Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China

    Chenqi Mou

Authors
  1. Chenqi Mou
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  2. Jiahua Lai
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Correspondence to Chenqi Mou .

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Editors and Affiliations

  1. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

  2. IMJ-PRG, Sorbonne University, Paris, France

    Elias Tsigaridas

  3. Institute of Information Technologies, Gebze Technical University, Gebze, Turkey

    Zafeirakis Zafeirakopoulos

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Mou, C., Lai, J. (2020). On the Chordality of Simple Decomposition in Top-Down Style. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_12

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  • DOI: https://doi.org/10.1007/978-3-030-43120-4_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43119-8

  • Online ISBN: 978-3-030-43120-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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