2020 Fiscal Year Final Research Report
Matching, matroid, and traveling salesman problem
| Project/Area Number |
16K16012
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical informatics
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| Research Institution | Hosei University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Keywords | マトロイド / 巡回セールスマン問題 / マッチング / 有向木 / 混雑ゲーム / 制約付き 2-マッチング |
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| Outline of Final Research Achievements |
The traveling salesman problem (TSP) is perhaps the most famous NP-hard problem, and has enhanced developments of many methods in the field of discrete optimization. In particular, TSP attracts recent intensive attention: several theoretical breakthrough papers have been published in this past decade.
Our research has intended to be applied in theoretical improvement in solving TSP. Specifically, our research has achieved deepening and extending of matching theory and matroid theory, which form bases of efficient solutions to discrete optimization problems. All of our 20 papers has been accepted to reputable, international, peer-reviewed journals or conferences, including top journals and conferences in the field of optimization.
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| Free Research Field |
離散最適化
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題で発表した 20 篇の論文のうち，巡回セールスマン問題 (TSP) に特に関連する論文として，クラスター巡回セールスマン問題という TSP の一般化に対する近似率を改善したものや，TSP の緩和問題である制約付き 2-マッチング問題などの数多くの概念を含む，グラフ上の最適化問題の枠組を提案したものがある．
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