2023 Fiscal Year Final Research Report

Development of Combinatorial Reconfiguration by Mathematics Approach: From Examples to New Methods

Planned Research

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Project Area	Fusion of Computer Science, Engineering and Mathematics Approaches for Expanding Combinatorial Reconfiguration
Project/Area Number	20H05795
Research Category	Grant-in-Aid for Transformative Research Areas (B)
Allocation Type	Single-year Grants
Review Section	Transformative Research Areas, Section (IV)
Research Institution	The University of Electro-Communications
Principal Investigator	OKAMOTO Yoshio 電気通信大学, 大学院情報理工学研究科, 教授 (00402660)
Co-Investigator(Kenkyū-buntansha)	神山直之九州大学, マス・フォア・インダストリ研究所, 教授 (10548134) 小関健太横浜国立大学, 大学院環境情報研究院, 准教授 (10649122) 垣村尚徳慶應義塾大学, 理工学部(矢上), 准教授 (30508180) 小林佑輔京都大学, 数理解析研究所, 准教授 (40581591) 野崎雄太広島大学, 先進理工系科学研究科(理), 助教 (40822648) 岩政勇仁京都大学, 情報学研究科, 助教 (70854602) 前澤俊一東京理科大学, 理学部第二部数学科, 助教 (70905934)
Project Period (FY)	2020-10-02 – 2023-03-31
Keywords	組合せ遷移 / 数学 / 離散数学 / アルゴリズム / 計算複雑性
Outline of Final Research Achievements	During the research project period (including the extension), we obtained 89 papers, 52 presentations, and 2 books. Below are summaries of two notable results. (1) In the study of systematic collections of mathematical utility in combinatorial reconfiguration, we explored a combinatorial reconfiguration problem from algorithmic game theory. We conducted a computational complexity analysis and designed an efficient algorithm. This work was presented at the prestigious AAAI 2022 conference. (2) In developing mathematical methodologies for combinatorial reconfiguration, we investigated a graph-theoretic problem. Our research introduced a novel method based on combinatorial reconfiguration, which proved a well-known theorem in graph theory literature. This work was presented at the prestigious SODA 2022 conference.
Free Research Field	数学
Academic Significance and Societal Importance of the Research Achievements	組合せ遷移の研究に資する数学理論の構築に向けて，大きな成果を得ることができた．また，他の計画研究 (計算機科学のA01班，工学のB01班) と相補的な協働をすることで，組合せ遷移の社会実装に近づくことができた．国内における研究普及活動に加えて，国際ワークショップの主催，国際会議での発表を通じて，組合せ遷移研究における日本の研究者のリーダーシップとプレゼンスを強化することができた．