Combinatorial Approach to Algebraic Extension of Matching Problems

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K23323
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 1001:Information science, computer engineering, and related fields
• Research Institution: Kyoto University
• Principal Investigator: Iwamasa Yuni 京都大学, 情報学研究科, 助教 (70854602)
• Project Period (FY): 2020-09-11 – 2024-03-31
• Keywords: マッチング問題 / マトロイド / 代数的組合せ最適化 / 多項式時間可解性

Outline of Final Research Achievements

In this research project, we study (Weighted) Edmonds problem --- a problem of computing the rank of a matrix having symbols --- and its noncommutative variant. We devise an efficient and combinatorial algorithm for the case where the given matrix can be partitioned into 2x2 matrices. Based on this result, we also develop a strongly polynomial-time algorithm for computing the sequence of the maximum degree of Dieudonne minors of linear symbolic monomial matrices in the noncommutative setting.

Free Research Field

組合せ最適化

Academic Significance and Societal Importance of the Research Achievements

近年盛んに研究が行われている「代数的組合せ最適化」とよばれる分野において，組合せ的なアプローチで簡潔かつ高速なアルゴリズムの構築や「良い特徴づけ」となりうる新たな最大最小定理の導出を行ったことで，問題の数理構造そのものへの理解を深めることができた．これにより組合せ最適化分野のさらなる発展が期待できる．