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Algebraic constructions for combinatorial designs and their applications to combinatorial testing

Research Project

Project/Area Number 19K14585
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12030:Basic mathematics-related
Research InstitutionUniversity of Yamanashi

Principal Investigator

Lu Xiao-Nan  山梨大学, 大学院総合研究部, 特任助教 (10805683)

Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsCombinatorial design / Combinatorial testing / Locating array / Orthogonal array / Steiner quadruple system / Fault location / Adaptive algorithm / Error-correcting code / 適応型アルゴリズム / 特定アルゴリズム / locating array / orthogonal array / 誤り訂正符号 / 巡回準直交配列 / error-correcting / 組合せ探索問題 / 組合せデザイン / Steiner Quadruple System / 組合せテスト / 巡回符号 / covering array / CAOA / Latin square / hypercube / combinatorial design / group testing / 検査計画 / 組合せ配列 / Steiner system
Outline of Research at the Start

本研究は,離散数学の一分野である組合デザイン理論において,特殊な代数的内部構造を持つ組合せ構造の存在性・構成問題を進展させ,これまでの研究を包含・拡張し,組合せデザインと関連する様々な構成法・代数的特徴付け・最適性などを研究対象とする.また,既知の組合せ構造とその構成法に対して,組合せ論的,代数的および幾何的性質の解明を通して,近年発展してきた検査計画という分野に適用することを目的とする.さらに,検査計画の理論研究を基に,大規模・複雑システムの開発に伴う,ソフトウェアテスト・ネットワークテストなどの応用研究において,より良いアルゴリズムの開発・改良が期待される.

Outline of Final Research Achievements

Focusing on algebraic constructions of combinatorial designs, this research is devoted for clarifying the relationship among different algebraic constructions, and exploring the applications of those combinatorial designs. In particular, for combinatorial interaction testing, both new constructions of combinatorial arrays and improved faulty location algorithms are developed. Main contributions include: (1) Generalization of mutually orthogonal Latin squares to higher dimensions; (2) Proof of existence of abelian-group invariant Steiner quadruple systems; (3) Algebraic characterization, statical optimality, new results and classifications by computer search for circulant almost orthogonal arrays; (4) Clarifying the linear dimensions of a class of BCH codes with large distance. (5) Proposing a new bound for locating arrays. (6) Improving adaptive algorithms for fault location in combinatorial testing; (7) Introducing the notion and constructions of error-correcting locating arrays.

Academic Significance and Societal Importance of the Research Achievements

本研究では,組合せデザインと呼ばれる離散構造の代数的側面に焦点を当てて,それらの内在する関連性の解明およびそれらの符号および統計的実験計画への応用について研究を行って,各問題に新たな研究結果を得た.また,複数のコンポーネントが組み込まれる複雑システムにおける故障を検出するための数理モデルとして,組合せデザイン・代数学・符号理論等多様な手法を用いて,検査計画問題の理論的限界のより精確な評価を与え,検出アルゴリズムの効率化に成功した.本研究で得られた成果は,情報通信・実験計画・ソフトウェア工学等の領域において,基礎数学理論・数理モデルおよび関連するアルゴリズムを貢献することになる.

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (19 results)

All 2022 2021 2020 2019 Other

All Int'l Joint Research (2 results) Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 3 results) Presentation (9 results) (of which Int'l Joint Research: 2 results,  Invited: 4 results)

  • [Int'l Joint Research] Soochow University (蘇州大学)(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] 蘇州大学(中国)

    • Related Report
      2019 Research-status Report
  • [Journal Article] An Improved Adaptive Algorithm for Locating Faulty Interactions in Combinatorial Testing2022

    • Author(s)
      Qianqian Yang, Xiao-Nan Lu
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E105.A Issue: 6 Pages: 930-942

    • DOI

      10.1587/transfun.2021EAP1071

    • NAID

      130008121543

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2022-06-01
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Error-correcting locating arrays for interaction fault location in combinatorial testing2022

    • Author(s)
      Xiao-Nan Lu, Masakazu Jimbo
    • Journal Title

      Proceedings of the 2022 IEEE International Symposium on Information Theory (ISIT)

      Volume: 採択

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal and efficient designs for fMRI experiments via two-level circulant almost orthogonal arrays2021

    • Author(s)
      Xiao-Nan Lu, Miwako Mishima, Nobuko Miyamoto, Masakazu Jimbo
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 213 Pages: 33-49

    • DOI

      10.1016/j.jspi.2020.11.005

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] BCH codes with minimum distance proportional to code length2021

    • Author(s)
      Satoshi Noguchi, Xiao-Nan Lu, Masakazu Jimbo, Ying Miao
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 35 Issue: 1 Pages: 179-193

    • DOI

      10.1137/19m1260876

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Symmetric abelian group-invariant Steiner quadruple systems2021

    • Author(s)
      Lijun Ji, Xiao-Nan Lu
    • Journal Title

      Journal of Combinatorial Theory, Series A

      Volume: 181 Pages: 1-21

    • DOI

      10.1016/j.jcta.2021.105435

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On Dimensionally Orthogonal Diagonal Hypercubes2020

    • Author(s)
      Xiao-Nan Lu, Tomoko Adachi
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E103.A Issue: 10 Pages: 1211-1217

    • DOI

      10.1587/transfun.2019DMP0009

    • NAID

      130007920249

    • ISSN
      0916-8508, 1745-1337
    • Year and Date
      2020-10-01
    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On dimensionally orthogonal diagonal hypercubes2020

    • Author(s)
      X.-N. Lu and T. Adachi
    • Journal Title

      IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

      Volume: E103-A

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Arrays for combinatorial interaction testing: a review on constructive approaches2019

    • Author(s)
      X.-N. Lu and M. Jimbo
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: 2 Issue: 2 Pages: 641-667

    • DOI

      10.1007/s42081-019-00056-w

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] Almost external difference families via cyclotomy2022

    • Author(s)
      盧 暁南, 川口 翔大, 三嶋 美和子
    • Organizer
      日本数学会2022年度年会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Circulant almost orthogonal arrays: statistical optimality and related combinatorial structures2022

    • Author(s)
      Xiao-Nan Lu, Miwako Mishima, Nobuko Miyamoto, Masakazu Jimbo
    • Organizer
      Colloquium on Combinatorial Designs
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Circulant almost orthogonal arrays and related problems in statistics and combinatorics2021

    • Author(s)
      Xiao-Nan Lu, Miwako Mishima, Nobuko Miyamoto, Masakazu Jimbo
    • Organizer
      Xinyang Normal University Math and Statistics Colloquium
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] SATソルバーの組合せデザイン問題への応用事例2021

    • Author(s)
      盧 暁南
    • Organizer
      名古屋組合せ論セミナー
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Searching for edges in a multi-partite graph2021

    • Author(s)
      盧 暁南
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Almost external difference families via cyclotomy2021

    • Author(s)
      Xiao-Nan Lu, Shota Kawaguchi, Miwako Mishima
    • Organizer
      43rd Australasian Combinatorics Conference
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Enumeration and classification of two-level circulant almost orthogonal arrays with strength 2 and bandwidth 12021

    • Author(s)
      盧 暁南
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Circulant almost orthogonal arrays and perfect binary sequences2020

    • Author(s)
      盧 暁南,三嶋美和子,宮本暢子,神保雅一
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] グループテスト入門2019

    • Author(s)
      盧 暁南
    • Organizer
      研究集会「実験計画法と符号および関連する組合せ構造」2019
    • Related Report
      2019 Research-status Report
    • Invited

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Published: 2019-04-18   Modified: 2023-01-30  

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