| Project/Area Number |
10680429
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
社会システム工学
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| Research Institution | Osaka University |
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Principal Investigator |
FUJISHIGE Satoru Osaka University, Graduate School of Engineering Science, Professor, 大学院・基礎工学研究科, 教授 (10092321)
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| Project Period (FY) |
1998 – 1999
|
| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥2,600,000 (Direct Cost: ¥2,600,000)
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| Keywords | Submodular functions / Combinatorial optimization / Discrete Algorithms |
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| Research Abstract |
The most important result of this project is the combinatorial, strongly polynomial-time algorithm for minimizing submodular functions. It has been a long-standing open problem to obtain such a combinatorial algorithm since 1981. With the aid of this algorithm we can construct efficient algorithms for a lot of combinatorial optimization problems such as the submodular flow problem for which existing algorithms assume the oracle for submodular function minimization.
Moreover, we have obtained the following results. We gave a short proof of the validity of M. Queyranne's algorithm for minimizing symmetric submodular functions. We proposed an algorithm for minimizing submodular functions arising from concave functions by means of parametric max-flow algorithms. We also showed the laminarity property of posi-modular functions, which generalize symmetric submodular functions. Furthermore, we proved that the dual greedy polyhedra investigated by Faigle and Kern belong to the class of submodular flow polyhedra. Concerning the minimum-norm point problem, related to submodular function minimization, we proposed an efficient algorithm for finding the minimum-norm point in the intersection of the convex hull of points and an affine space.
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