2016 Fiscal Year Final Research Report
Deepening analysis methods for limits of computation through integration with optimization techniques
Project Area | A multifaceted approach toward understanding the limitations of computation |
Project/Area Number |
24106005
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Research Category |
Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
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Allocation Type | Single-year Grants |
Review Section |
Science and Engineering
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Research Institution | Kwansei Gakuin University (2015-2016) Kyoto University (2012-2014) |
Principal Investigator |
Katoh Naoki 関西学院大学, 理工学部, 教授 (40145826)
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Co-Investigator(Kenkyū-buntansha) |
岩田 覚 東京大学, 大学院情報処理工学系研究科, 教授 (00263161)
岡本 吉央 電気通信大学, 大学院情報理工学研究科, 准教授 (00402660)
神山 直之 九州大学, マス・フォア・インダストリ研究所, 准教授 (10548134)
来嶋 秀治 九州大学, 大学院システム情報科学研究院, 准教授 (70452307)
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Project Period (FY) |
2012-06-28 – 2017-03-31
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Keywords | 最適化理論 / 拡張定式化 / 疎性マトロイド / マトロイド・パリティ問題 / 計算限界分析 / #P困難 / 体積計算 |
Outline of Final Research Achievements |
In this project, we obtained the following results. 1. On extended formulations that have been extensively studied recently, a compact representation is provided for sparsity matroids that play important roles both in theory and in practice. 2. The first polynomial-time algorithm is developed for the weighted linear matroid parity problem. 3. A novel reduction method (a hardness proof method) is developed among problems for which brute-force searches cannot be essentially surpassed, resulting in a new standard for the field of exponential-time computation. 4. A polynomial time deterministic approximation algorithm is presented to compute the volume of a 0-1 knapsack polytope which is known to be #P-hard.
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Free Research Field |
組合せ最適化
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