2019 Fiscal Year Final Research Report
Development of practical combinatorial optimization algorithms by speeding up the continuous relaxation method
| Project/Area Number |
17K00040
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical informatics
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| Research Institution | Chuo University (2019)
Institute of Physical and Chemical Research (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 近似アルゴリズム / 最適化 / クラスタリング / 劣モジュラ最適化 |
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| Outline of Final Research Achievements |
This project aims at developing practical efficient approximation algorithms for hard combinatorial optimization problems by the continuous relaxation method. The continuous relaxation method has advantages in flexibility and usability. Simultaneously, it has a disadvantage in the computational speed. To obtain practical approximation algorithms, the project worked on this issue by investigating formulations of continuous relaxations and by studying fast algorithms for solving continuous relaxations. As accomplishments of the project, we obtain new algorithms for various combinatorial optimization problems such as hypergraph correlation clustering problem, stochastic submodular maximization problem under knapsack constraints, and generalized budget allocation problem.
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| Free Research Field |
組合せ最適化
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| Academic Significance and Societal Importance of the Research Achievements |
本研究により，多くの組合せ最適化問題について実用的なアルゴリズムを得ることができた．また，未知の組合せ最適化問題を効率的に解くための理論基盤になるような知見を得ることもできた．組合せ最適化問題は，ロジスティクスなどの産業分野から機械学習のような人工知能技術まで多様な場面で現れるので，組合せ最適化問題を解く効率的なアルゴリズムの実用化は利便性の高い情報システム実現につながる重要な成果である．
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