2011 Fiscal Year Final Research Report
Development of Efficient and Accurate Approximation Algorithms for Constrained Optimization of Discrete Convex Functions
| Project/Area Number |
21740060
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tohoku University |
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Principal Investigator |
SHIOURA Akiyoshi 東北大学, 大学院・情報科学研究科, 准教授 (10296882)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 離散最適化 / 組合せ最適化 / 数理計画 / 離散凸関数 / 近似アルゴリズム / アルゴリズム / マトロイド / 劣モジュラ関数 |
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| Research Abstract |
The aim of this research is to develop algorithms with theoretical guarantee for both of computational time and quality of solutions by using the theory of discrete convex analysis. During the three years of the research period, I have obtained various new results. In particular, I developed a polynomial-time approximation scheme for the maximization of an M-concave function under multiple knapsack constraints. In addition, I revealed the structure of a general solution set called a neighbor system, and showed that the minimization of a separable-convex function over a neighbor system can be solved in polynomial time.
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Research Products
(13 results)
