On solving linear systems with combinatorial constraints

2023 Fiscal Year Final Research Report

• Project/Area Number: 17K12646
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Tokyo Institute of Technology (2020-2023); Tokyo Metropolitan University (2018-2019); National Institute of Informatics (2017)
• Principal Investigator: Sumita Hanna 東京工業大学, 情報理工学院, 准教授 (10761356)
• Project Period (FY): 2017-04-01 – 2024-03-31
• Keywords: マトロイド / 公平割当 / オンライン最適化

Outline of Final Research Achievements

We aim to solve optimization problems that can be represented as linear systems with combinatorial constraints. Fundamental constraints in the field of combinatorial optimization include matroid and knapsack constraints. We focus on problems with those constraints. In this project, we proposed efficient algorithms with theoretical analysis for the optimal matroid partition problem, robust combinatorial optimization problems, the fair allocation problem, and so on. We also worked on an unexpected direction such as online optimization.

Free Research Field

組合せ最適化

Academic Significance and Societal Importance of the Research Achievements

本研究課題は主に組合せ最適化の理論的側面の研究であるが，ニーズによっては実応用も期待できる．例えば，本研究で取り組んだロバスト組合せ最適化問題には，セキュリティゲームといった実応用をもつ問題も含まれる．また，本研究のトピックの中には今後新たな問題の枠組みとして発展が期待できるものもあり，本研究課題の成果はその一ステップになると考えている．
本研究の成果は，理論計算機科学や人工知能分野における査読付き国際会議および論文誌で発表している．