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マトロイド理論・離散凸解析理論に基づく社会システム解析理論の構築

Research Project

Project/Area Number 20K11699
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60020:Mathematical informatics-related
Research InstitutionHosei University

Principal Investigator

高澤 兼二郎  法政大学, 理工学部, 教授 (10583859)

Project Period (FY) 2020-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsアルゴリズム的ゲーム理論 / マトロイド / 純粋ナッシュ均衡 / 混雑ゲーム / 離散凸最適化 / ポピュラー有向木 / アルゴリズム / 離散凸解析 / 有向森 / 公平分割 / 社会的最適解
Outline of Research at the Start

本研究は,離散凸解析の立場から,劣モジュラ理論における機械学習に相当する応用分野をマトロイド理論に対して開拓し,マトロイド理論の応用研究を加速させるものである.
具体的な研究内容としては,社会システム解析理論の構築に取り組む.離散凸解析のこれまでの応用研究の中で,マトロイドやM凸関数の理論は経済やゲーム理論との親和性が高いことが知られている.本研究は,これらの既存研究の流れを継承・推進しつつ,マトロイド理論の新たな応用先を開拓するものである.

Outline of Annual Research Achievements

本年度の研究成果のうち,本研究課題において特に重要なものは,論文「Pure Nash equilibria in weighted congestion games with complementarities and beyond」である.
混雑ゲーム(congestion game)とは,非協力ゲームの純粋ナッシュ均衡の研究における主要なモデルである.混雑ゲームを一般化するモデルの中に,重み付き混雑ゲーム(weighted congestion game),および,相補性混雑ゲーム(congestion game with complementarities)がある.これらのモデルにおいては,様々な仮定のもとで,純粋ナッシュ均衡の存在性が証明されている.仮定の中には,各プレイヤーの戦略空間がマトロイドの基族であることや,コスト関数がある種の単調性をもつことなどがある.
本論文では,重み付き混雑ゲームと相補性混雑ゲームを共通に一般化するモデルを提案した.さらに,本モデルにおいて,各プレイヤーの戦略空間がマトロイドの基族であり,コスト関数がより簡易に定義される単調性をもつという仮定のもとで,純粋ナッシュ均衡の存在性を証明した.本論文は,マルチエージェント分野の主要国際会議である The 23rd International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2024) に採択された.
その他,マトロイドに関する最大最小問題を扱った論文が査読付き国際論文誌に採録された.また,マトロイドを一般化する数理構造に注目したグラフ上の最適化を扱った論文,および,グラフ上の最適化アルゴリズムを用いたスケジューリングに関する論文を発表した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

上記のとおり,アルゴリズム的ゲーム理論およびマトロイドに関する複数の論文が,査読付き国際論文誌に採録,および,査読付き国際会議に採択された.
その一方で,新たに遂行中の研究で,時間的な制約から論文の発表が遅れているものがある.

Strategy for Future Research Activity

次年度は本研究課題の最終年度であるため,新たな研究を遂行するとともに,これまでに遂行してきた研究を取りまとめ,論文として発表する予定である.

Report

(4 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (35 results)

All 2024 2023 2022 2021 2020 Other

All Journal Article (17 results) (of which Int'l Joint Research: 2 results,  Open Access: 5 results,  Peer Reviewed: 15 results) Presentation (16 results) (of which Int'l Joint Research: 6 results) Remarks (2 results)

  • [Journal Article] Pure Nash equilibria in weighted congestion games with complementarities and beyond2024

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2024)

      Volume: - Pages: 2495-2497

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on upgrading the min–max weight of a base of a matroid2024

    • Author(s)
      Yukiya Hatajima, Kenjiro Takazawa
    • Journal Title

      JSIAM Letters

      Volume: 16 Issue: 0 Pages: 1-4

    • DOI

      10.14495/jsiaml.16.1

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Finding a Maximum Restricted t-Matching via Boolean Edge-CSP2023

    • Author(s)
      Yuni Iwamasa, Yusuke Kobayashi, Kenjiro Takazawa
    • Journal Title

      arXiv

      Volume: -

    • Related Report
      2023 Research-status Report
    • Open Access
  • [Journal Article] A Faster Deterministic Approximation Algorithm for TTP-22023

    • Author(s)
      Yuga Kanaya, Kenjiro Takazawa
    • Journal Title

      arXiv

      Volume: -

    • Related Report
      2023 Research-status Report
    • Open Access
  • [Journal Article] An efficient algorithm for minimizing M-convex functions under a color-induced budget constraint2023

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      Operations Research Letters

      Volume: 51 Issue: 2 Pages: 128-132

    • DOI

      10.1016/j.orl.2023.01.003

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finding popular branchings in vertex-weighted directed graphs2023

    • Author(s)
      Kei Natsui, Kenjiro Takazawa
    • Journal Title

      Theoretical Computer Science

      Volume: 953 Pages: 113799-113799

    • DOI

      10.1016/j.tcs.2023.113799

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Minimizing submodular functions on diamonds via generalized fractional matroid matchings2022

    • Author(s)
      Fujishige Satoru、Kiraly Tamas、Makino Kazuhisa、Takazawa Kenjiro、Tanigawa Shin-ichi
    • Journal Title

      Journal of Combinatorial Theory, Series B

      Volume: 157 Pages: 294-345

    • DOI

      10.1016/j.jctb.2022.07.005

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An improved heuristic algorithm for the maximum benefit Chinese postman problem2022

    • Author(s)
      Shiori Matsuura, Kenjiro Takazawa
    • Journal Title

      RAIRO - Operations Research

      Volume: 56 Issue: 3 Pages: 1283-1291

    • DOI

      10.1051/ro/2022044

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A common generalization of budget games and congestion games2022

    • Author(s)
      Fuga Kiyosue, Kenjiro Takazawa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 13584 Pages: 258-274

    • DOI

      10.1007/978-3-031-15714-1_15

    • ISBN
      9783031157134, 9783031157141
    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Posimodular Function Optimization2022

    • Author(s)
      Magnus M. Halldorsson, Toshimasa Ishii, Kazuhisa Makino, Kenjiro Takazawa
    • Journal Title

      Algorithmica

      Volume: 84 Issue: 4 Pages: 1107-1131

    • DOI

      10.1007/s00453-021-00910-y

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Notes on equitable partitions into matching forests in mixed graphs and into b-branchings in digraphs2022

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      Discrete Mathematics and Theoretical Computer Science

      Volume: 24 Issue: Graph Theory

    • DOI

      10.46298/dmtcs.8719

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Excluded t-factors in bipartite graphs: A unified framework for nonbipartite matchings, restricted 2-matchings, and matroids2022

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 36 Issue: 1 Pages: 702-727

    • DOI

      10.1137/18m1176737

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finding popular branchings in vertex-weighted digraphs2022

    • Author(s)
      Kei Natsui, Kenjiro Takazawa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 13174 Pages: 303-314

    • DOI

      10.1007/978-3-030-96731-4_25

    • ISBN
      9783030967307, 9783030967314
    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Optimal matroid bases with intersection constraints: Valuated matroids, M-convex functions, and their applications2021

    • Author(s)
      Yuni Iwamasa, Kenjiro Takazawa
    • Journal Title

      Mathematical Programming

      Volume: - Issue: 1-2 Pages: 229-256

    • DOI

      10.1007/s10107-021-01625-2

    • Related Report
      2022 Research-status Report 2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] The b-bibranching problem: TDI system, packing, and discrete convexity2021

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      Networks

      Volume: - Issue: 1 Pages: 32-46

    • DOI

      10.1002/net.22035

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Relationship of two formulations for shortest bibranchings2020

    • Author(s)
      K. Murota, K. Takazawa
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 38 Issue: 1 Pages: 141-161

    • DOI

      10.1007/s13160-020-00432-0

    • NAID

      210000178025

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Notes on equitable partitions into matching forests in mixed graphs and b-branchings in digraphs2020

    • Author(s)
      Kenjiro Takazawa
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 12176 Pages: 214-224

    • DOI

      10.1007/978-3-030-53262-8_18

    • ISBN
      9783030532611, 9783030532628
    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Presentation] Pure Nash equilibria in weighted congestion games with complementarities and beyond2024

    • Author(s)
      Kenjiro Takazawa
    • Organizer
      The 23rd International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2024)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] A faster deterministic approximation algorithm for TTP-22024

    • Author(s)
      Yuga Kanaya, Kenjiro Takazawa
    • Organizer
      The 8th International Symposium on Combinatorial Optimization (ISCO 2024)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] 巡回トーナメント問題に対する1+11/n近似アルゴリズム2023

    • Author(s)
      金谷祐河, 高澤兼二郎
    • Organizer
      日本オペレーションズ・リサーチ学会研究部会「最適化の理論とアルゴリズム」未来を担う若手研究者の集い 2023
    • Related Report
      2023 Research-status Report
  • [Presentation] 巡回トーナメント問題に対する近似アルゴリズムの改良2023

    • Author(s)
      金谷祐河, 高澤兼二郎
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Related Report
      2023 Research-status Report 2022 Research-status Report
  • [Presentation] 制限付きt-マッチング問題に対する制約充足的アプローチ2023

    • Author(s)
      岩政勇仁, 小林佑輔, 高澤兼二郎
    • Organizer
      アルゴリズム研究発表会
    • Related Report
      2023 Research-status Report
  • [Presentation] 巡回トーナメント問題に対する近似アルゴリズムの改良2023

    • Author(s)
      金谷祐河, 高澤兼二郎
    • Organizer
      日本応用数理学会第 19 回研究部会連合発表会
    • Related Report
      2022 Research-status Report
  • [Presentation] 全域木における最小の最大辺重みを改善する問題の一般化2023

    • Author(s)
      畑島志哉, 高澤兼二郎
    • Organizer
      日本応用数理学会第 19 回研究部会連合発表会
    • Related Report
      2022 Research-status Report
  • [Presentation] A common generalization of budget games and congestion games2022

    • Author(s)
      Fuga Kiyosue, Kenjiro Takazawa
    • Organizer
      The 15th International Symposium on Algorithmic Game Theory (SAGT 2022)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] 予算ゲームと混雑ゲームの共通の一般化2022

    • Author(s)
      清末風雅, 高澤兼二郎
    • Organizer
      電子情報通信学会コンピュテーション研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] 重みつきポピュラー有向木のアルゴリズム2022

    • Author(s)
      夏井慧, 高澤兼二郎
    • Organizer
      日本オペレーションズ・リサーチ学会研究部会「最適化手法とアルゴリズム ─未来を担う若手研究者の集い 2022─」
    • Related Report
      2021 Research-status Report
  • [Presentation] Finding popular branchings in vertex-weighted digraphs2022

    • Author(s)
      Kei Natsui, Kenjiro Takazawa
    • Organizer
      The 16th International Conference and Workshops on Algorithms and Computation (WALCOM 2022)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 重みつきポピュラー有向木のアルゴリズム2022

    • Author(s)
      夏井慧, 高澤兼二郎
    • Organizer
      日本オペレーションズ・リサーチ学会 2022 年春季研究発表会
    • Related Report
      2021 Research-status Report
  • [Presentation] 予算ゲームの一般化におけるナッシュ均衡2022

    • Author(s)
      清末風雅, 高澤兼二郎
    • Organizer
      日本応用数理学会第 18 回研究部会連合発表会
    • Related Report
      2021 Research-status Report
  • [Presentation] Optimal matroid bases with intersection constraints: Valuated matroids, M-convex functions, and their applications2020

    • Author(s)
      Yuni Iwamasa, Kenjiro Takazawa
    • Organizer
      The 16th Annual Conference on Theory and Applications of Models of Computation (TAMC 2020)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Notes on equitable partitions into matching forests in mixed graphs and b-branchings in digraphs2020

    • Author(s)
      Kenjiro Takazawa
    • Organizer
      The 6th International Symposium on Combinatorial Optimization (ISCO 2020)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] 交叉制約下でのマトロイドの最適基とその一般化2020

    • Author(s)
      岩政勇仁, 高澤兼二郎
    • Organizer
      京都大学数理解析研究所 共同研究(グループ型) 数理最適化の理論・アルゴリズム・応用
    • Related Report
      2020 Research-status Report
  • [Remarks] Publications by Kenjiro Takazawa

    • URL

      https://ds.ws.hosei.ac.jp/papers_j.html

    • Related Report
      2023 Research-status Report
  • [Remarks] Publications by Kenjiro Takazawa

    • URL

      http://ds.ws.hosei.ac.jp/papers_j.html

    • Related Report
      2022 Research-status Report 2021 Research-status Report

URL: 

Published: 2020-04-28   Modified: 2024-12-25  

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