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Algorithms for combinatorial problems based on commutative algebra

Research Project

Project/Area Number 23500025
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Fundamental theory of informatics
Research InstitutionTokyo University of Science

Principal Investigator

SATO Yosuke  東京理科大学, 理学部, 教授 (50257820)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsブーリアン・グレブナー基底 / 組み合わせ問題 / 数独問題の難易度 / ブーリアン・グレブナー基 底
Research Abstract

We investigated a theory of commutative algebra that is needed for a solution algorithm for combinatorial problems. We have concentrated on problems which do not essentially contain integer arithmetic. As a result, we found that our algorithm based on Boolean Groebner bases methods is the best method.We also implemented our method on the computer algebra system Risa/Asir and showed the efficiency of our algorithm, especially our algorithm is more practical on the environment of parallel computations.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (22 results)

All 2014 2013 2012 2011

All Journal Article (9 results) (of which Peer Reviewed: 4 results) Presentation (13 results)

  • [Journal Article] 数独の難易度判定のためのブーリアングレブナー基底の並列計算について2013

    • Author(s)
      佐藤裕介, 井上秀太郎, 佐藤洋祐
    • Journal Title

      数理解析研究所講究録

      Volume: 第1843巻 Pages: 28-37

    • Related Report
      2013 Final Research Report
  • [Journal Article] 代数的閉体における限量子消去アルゴリズムについて2013

    • Author(s)
      深作亮也, 井上秀太郎, 佐藤洋祐
    • Journal Title

      COE Lecture Note

      Volume: Vol.49 Pages: 27-32

    • Related Report
      2013 Final Research Report
  • [Journal Article] On QE Algorithms over Algebraically Closed Field2013

    • Author(s)
      Ryoya Fukasaku, Shutaro Inoue and Yosuke Sato
    • Journal Title

      Proceedings of Fifth International Conference on Mathematical Aspects of Computer and Information Sciences

      Pages: 21-25

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 代数的閉体における限量子消去アルゴリズムについて2013

    • Author(s)
      深作亮也、井上秀太郎、佐藤洋祐
    • Journal Title

      COE Lecture Note

      Volume: 49 Pages: 27-32

    • Related Report
      2013 Annual Research Report
  • [Journal Article] On QE Algorithms over Algebraically Closed Field2013

    • Author(s)
      Ryoya Fukasaku,Shutaro Inoue,Yosuke Sato
    • Journal Title

      Proceedings of the Fifth International Conference on MACIS2013

      Volume: 1 Pages: 21-25

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] グレブナー基底を使った数独の難易度判定と問題作成2012

    • Author(s)
      井上秀太郎, 佐藤洋祐
    • Journal Title

      数理解析研究所講究録

      Volume: 第1785巻 Pages: 51-56

    • Related Report
      2013 Final Research Report
  • [Journal Article] グレブナー基底を使った数独の難易度判定と問題作成2012

    • Author(s)
      井上秀太郎、佐藤洋祐
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1785号 Pages: 51-56

    • Related Report
      2012 Research-status Report
  • [Journal Article] Boolean Gröbner Bases2011

    • Author(s)
      Yosuke Sato, Shutaro Inoue, Akira Suzuki, Katsusuke Nabeshima and Ko Sakai
    • Journal Title

      Journal of Symbolic Computation

      Volume: Vol46/5 Pages: 622-632

    • NAID

      120007130919

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Boolean Groebner Bases2011

    • Author(s)
      Yosuke Sato, Shutaro Inoue, Akira Suzuki, Katsusuke Nabeshima & Ko Sakai
    • Journal Title

      Journal of Symbolic Computation

      Volume: Vol 46/5 Pages: 622-632

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Complex QE の並列計算アルゴリズム2014

    • Author(s)
      深作亮也、佐藤洋祐
    • Organizer
      日本数式処理学会 東北地区合同分科会
    • Place of Presentation
      仙台青葉カルチャーセンター
    • Related Report
      2013 Annual Research Report
  • [Presentation] Complex QE について2013

    • Author(s)
      深作亮也、井上秀太郎、佐藤洋祐
    • Organizer
      第22回日本数式処理学会大会
    • Place of Presentation
      防衛大学校
    • Related Report
      2013 Annual Research Report
  • [Presentation] Stability of Groebner Bases in Terms of a Commutative von Neumann Regular Ring2012

    • Author(s)
      Yosuke Sato
    • Organizer
      The Tenth Asian Symposium on Computer Mathematics
    • Year and Date
      2012-10-27
    • Related Report
      2013 Final Research Report
  • [Presentation] On parallel Computations of Boolean Groebner bases for combinatorial problems2012

    • Author(s)
      Shutaro Inoue and Yosuke Sato
    • Organizer
      Conference on Applications of Computer Algebra 2012
    • Year and Date
      2012-06-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Parallel Algebraic Computations for Combinatorial Problems2012

    • Author(s)
      Yosuke Sato and Shutaro Inoue
    • Organizer
      NII Shonan Meeting on Parallel Methods for Constraint Solving and Combinatorial Optimization
    • Year and Date
      2012-05-31
    • Related Report
      2013 Final Research Report
  • [Presentation] Why we need and how we compute parametric Groebner Bases2012

    • Author(s)
      Yosuke Sato
    • Organizer
      Bioinformatics Week in Odaiba
    • Year and Date
      2012-01-27
    • Related Report
      2013 Final Research Report
  • [Presentation] 数独の最小分岐数の計算について2012

    • Author(s)
      井上秀太郎, 佐藤洋祐
    • Organizer
      日本数式処理学会理論分科会及びシステム分科会合同研究会
    • Year and Date
      2012-01-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Parallel Algebraic Computations for Combinatorial Problems2012

    • Author(s)
      Yosuke Sato, Shutaro Inoue
    • Organizer
      NII Shonan Meeting on Parallel Methods for Constraint Solving and Combinatorial Optimization
    • Place of Presentation
      Shonan Village Center,Japan
    • Related Report
      2012 Research-status Report
  • [Presentation] An extension of the NTRU Cryptosystem2012

    • Author(s)
      Shutaro Inoue, Yosuke Sato
    • Organizer
      Conference on Applications of Computer Algebra 2012
    • Place of Presentation
      Sofia, Bulgaria
    • Related Report
      2012 Research-status Report
  • [Presentation] On parallel computations of Boolean Groebner bases for combinatorial problems2012

    • Author(s)
      Shutaro Inoue, Yosuke Sato
    • Organizer
      Conference on Applications of Computer Algebra 2012
    • Place of Presentation
      Sofia, Bulgaria
    • Related Report
      2012 Research-status Report
  • [Presentation] Stability of Groebner Bases in Terms of a Commutative von Neumann Regular Ring2012

    • Author(s)
      Yosuke Sato
    • Organizer
      The Asian Symposium on Computer Mathematics 2012
    • Place of Presentation
      Beijing,China
    • Related Report
      2012 Research-status Report
  • [Presentation] Maple等の数式処理システムを支える計算機代数アルゴリズム2012

    • Author(s)
      佐藤 洋祐
    • Organizer
      Maple Academic Conference 2012(数学編)
    • Place of Presentation
      アキバプラザ
    • Related Report
      2012 Research-status Report
  • [Presentation] Why we need and how we compute parametric Groebner Bases2012

    • Author(s)
      Yosuke Sato
    • Organizer
      Bioinformatics week in Odaiba 2011
    • Place of Presentation
      生命情報工学研究センター
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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