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2011 Fiscal Year Final Research Report

Structural Analysis of Mathematical Programming based on CombinatorialMatrix Theory

Research Project

  • PDF
Project/Area Number 21760057
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionThe University of Tokyo

Principal Investigator

KAKIMURA Naonori  東京大学, 教養学部, 特任講師 (30508180)

Project Period (FY) 2009 – 2011
Keywords組合せ最適化 / 定性的行列理論 / 疎性 / マッチング / グラフアルゴリズム / 点素サイクル
Research Abstract

Mathematical programming is a branch of mathematics concerned with optimization problems, in which one aims to find the best solution subject to some constraints, and it can be applied to a variety of engineering fields such as operations research. Combinatorial matrix theory is an approach to understand matrix structure using combinatorial methodology, which is useful for structural analysis of large linear systems in practice. In this research, we have analyzed mathematical programming problems based on combinatorial properties such as sign patterns or sparsity. In addition, we have developed combinatorial matrix theory in terms of mathematical programming applications.

  • Research Products

    (20 results)

All 2012 2011 2010 2009

All Journal Article (7 results) (of which Peer Reviewed: 6 results) Presentation (13 results)

  • [Journal Article] Packing Directed Circuits through Prescribed VerticesBounded-Fractionally2012

    • Author(s)
      Naonori Kakimura, and Ken-ichiKawarabayashi
    • Journal Title

      SIAM Journal onDiscrete Mathematics

      Volume: 26(3) Pages: pp.1121-1133

    • DOI

      DOI:10.1137/100786423

    • Peer Reviewed
  • [Journal Article] Packing Cycles through Prescribed Vertices under Modularity Constraints2012

    • Author(s)
      Naonori Kakimura and Ken-ichi Kawarabayashi
    • Journal Title

      Advances in Applied Mathematics

      Volume: 49(2) Pages: 97-110

    • DOI

      DOI:10.1016/j.aam.2012.03.002

    • Peer Reviewed
  • [Journal Article] Computing Knapsack Solutions with Cardinality Robustness2012

    • Author(s)
      Naonori Kakimura, Kazuhisa Makino, and Kento Seimi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 29(3) Pages: 469-483

    • DOI

      DOI:10.1007/s13160-012-0075-z

    • Peer Reviewed
  • [Journal Article] Packing Cycles through Prescribed Vertices2011

    • Author(s)
      Naonori Kakimura, Ken-ichi Kawarabayashi, and Daniel Marx
    • Journal Title

      Journal of Combinatorial Theory, Series B

      Volume: 101 Pages: 378-381

    • DOI

      DOI:10.1016/j.jctb.2011.03.004

    • Peer Reviewed
  • [Journal Article] 数理計画と組合せ的行列理論2011

    • Author(s)
      垣村尚徳
    • Journal Title

      オペレーションズ・リサーチ

      Volume: 56,No.1 Pages: 21-26

  • [Journal Article] Matching Structure of Symmetric Bipartite Graphs and a Generalization of Polya's Problem2010

    • Author(s)
      Naonori Kakimura
    • Journal Title

      Journal of Combinatorial Theory, Series B

      Volume: 100 Pages: 650-670

    • DOI

      DOI:10.1016/j.jctb.2010.06.003

    • Peer Reviewed
  • [Journal Article] A Direct Proof for the Matrix Decomposition of Chordal-Structured Positive Semidefinite Matrices2010

    • Author(s)
      Naonori Kakimura
    • Journal Title

      Linear Algebra and Its Applications

      Volume: 433 Pages: 819-823

    • DOI

      DOI:10.1016/j.laa.2010.04.012

    • Peer Reviewed
  • [Presentation] 疎な線形相補性問題に対する組合せ的アルゴリズム2012

    • Author(s)
      澄田範奈,垣村尚徳,牧野和久
    • Organizer
      2012年日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      ウインクあいち
    • Year and Date
      20120912-13
  • [Presentation] Computing Knapsack Solutions with Cardinality Robustness2012

    • Author(s)
      N. KAKIMURA, K. Makino, and K. Seimi
    • Organizer
      The 21th International Symposium on Mathematical Programming(ISMP)
    • Place of Presentation
      Berlin, Germany
    • Year and Date
      20120819-24
  • [Presentation] Erdos-Posa Property and Its Algorithmic Applications - Parity Constraints Subset Feedback Set, and Subset Packing2012

    • Author(s)
      N. Kakimura, K. Kawarabayashi, and Y. Kobayashi
    • Organizer
      The 23rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA2012)
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      20120117-19
  • [Presentation] Computing Knapsack Solutions with Cardinality Robustness2011

    • Author(s)
      N. Kakimura, K. Makino, and K. Seimi
    • Organizer
      The 22nd International Symposium on Algorithms and Computation (ISAAC 2011)
    • Place of Presentation
      Yokohama, Japan
    • Year and Date
      20111205-08
  • [Presentation] 河原林健一.指定された頂点を通るパリティ制約付サイクルのパッキング2011

    • Author(s)
      垣村尚徳
    • Organizer
      日本応用数理学会2011年度年会
    • Place of Presentation
      同志社大学
    • Year and Date
      20110914-16
  • [Presentation] Robust Independence Systems2011

    • Author(s)
      N. Kakimura and K. Makino
    • Organizer
      The 38th International Colloquium on Automata
    • Place of Presentation
      Languages and Programming (ICALP 2011), Zurich, Switzerland
    • Year and Date
      20110704-08
  • [Presentation] Set Covering with OrderedReplacement - Additive and Multiplicative Gaps2011

    • Author(s)
      F. Eisenbrand, N. Kakimura, T. Rothvoss, and L. Sanita
    • Organizer
      The 15th International Conference on Integer Programming and Combinatorial Optimization(IPCO 2011)
    • Place of Presentation
      Yorktown Heights, U.S
    • Year and Date
      20110615-17
  • [Presentation] Packing Cycles of Length 0 Modulo p through Prescribed Vertices2011

    • Author(s)
      N. Kakimura and K. Kawarabayashi
    • Organizer
      The 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      20110531-0603
  • [Presentation] Robust Independence Systems2011

    • Author(s)
      N. Kakimura and K. Makino
    • Organizer
      The SIAM Conference on Optimization
    • Place of Presentation
      Darmstadt, Germany
    • Year and Date
      20110516-19
  • [Presentation] ロバスト独立システム2011

    • Author(s)
      垣村尚徳,牧野和久
    • Organizer
      2011年日本オペレーションズ・リサーチ学会春季研究発表会
    • Place of Presentation
      電気通信大学
    • Year and Date
      20110317-18
  • [Presentation] 順序交換性を持つ集合被覆問題2011

    • Author(s)
      垣村尚徳(withF.Eisenbrand,T.RothvossandL.Sanita)
    • Organizer
      日本応用数理学会平成22年研究部会連合発表会
    • Place of Presentation
      電気通信大学
    • Year and Date
      20110307-08
  • [Presentation] コーダル構造を持つ半正定値対称行列に対する極大クリーク行列分解の直接的な証明2009

    • Author(s)
      垣村尚徳
    • Organizer
      2009年日本オペレーションズ・リサーチ学会秋季研究発表会
    • Place of Presentation
      長崎大学
    • Year and Date
      20090909-10
  • [Presentation] Matching Structure of Symmetric Bipartite Graphs and a Generalization of Polya's Problem2009

    • Author(s)
      N. Kakimura
    • Organizer
      The20th International Symposium on Mathematical Programming (ISMP)
    • Place of Presentation
      Chicago, U.S
    • Year and Date
      20090823-28

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Published: 2014-08-29  

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