2010 Fiscal Year Final Research Report
| Project/Area Number |
20740054
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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 | Kyoto University |
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Principal Investigator |
HIRAI Hiroshi Kyoto University, 大学院・情報理工学系研究科, 講師 (20378962)
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| Project Period (FY) |
2008 – 2010
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| Keywords | マルチフロー / メトリック / ネットワークフロー / 最大最小定理 |
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| Research Abstract |
We studied multiflow problems in combinatorial optimization. We introduced and developed the tight-span duality theory, which extends the duality relationship between multiflows and metrics, a well-known duality since 70's. As a consequence, We solved Karzanov' s problem, one of important open problems in the literature, which asks a complete characterization for the class of multiflow problems admitting combinatorial min-max theorems and the discreteness of flows. This result is an important step toward a unified theory for multiflow problems.
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