| Co-Investigator(Kenkyū-buntansha) |
牧野 和久 京都大学, 数理解析研究所, 教授 (60294162)
平井 広志 東京大学, 大学院情報理工学系研究科, 准教授 (20378962)
高澤 兼二郎 法政大学, 理工学部, 准教授 (10583859)
谷川 眞一 東京大学, 大学院情報理工学系研究科, 准教授 (30623540)
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| Budget Amount *help |
¥17,420,000 (Direct Cost: ¥13,400,000、Indirect Cost: ¥4,020,000)
Fiscal Year 2017: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
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| Outline of Final Research Achievements |
From the view points of the discrete structures associated with submodularity, we have investigated the theory and algorithms for discrete and combinatorial optimization problems which has been drawing researchers' attention in the world. We have developed a new theory of discrete convex functions, based on submodular structures, and effectively applied the theory to combinatorial and discrete optimization problems. We have also examined a general class of submodular-like discrete structures such as transversal-submodular functions and skew-bisubmodular functions. We then have shown fundamental min-max theorems for such discrete systems and investigated discrete algorithmic structures. We have also shown that the submodular structures play crucial roles in economy with indivisible commodities and a class of allocation problems in gaming situations.
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