Structural Analysis of Mathematical Programming based on CombinatorialMatrix Theory

2011 Fiscal Year Final Research Report

• Project/Area Number: 21760057
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Engineering fundamentals
• Research Institution: The 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

• [Journal Article] Packing Directed Circuits through Prescribed VerticesBounded-Fractionally (2012)
  • 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 Constraints (2012)
  • 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 Robustness (2012)
  • 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 Vertices (2011)
  • 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 Problem (2010)
  • 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 Matrices (2010)
  • 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 Robustness (2012)
  • 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 Packing (2012)
  • 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 Robustness (2011)
  • 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 Systems (2011)
  • 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 Gaps (2011)
  • 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 Vertices (2011)
  • 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 Systems (2011)
  • 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 Problem (2009)
  • Author(s): N. Kakimura
  • Organizer: The20th International Symposium on Mathematical Programming (ISMP)
  • Place of Presentation: Chicago, U.S
  • Year and Date: 20090823-28