| Project/Area Number |
16300002
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Kyoto University |
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Principal Investigator |
IWAMA Kazuo Kyoto University, Graduate School of Informatics, Professor (50131272)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Hiro Kyoto University, Graduate School of Informatics, Professor (50283487)
MIYAZAKI Shuichi Kyoto University, Academic Center for Computing and Media Studies, Associate Professor (00303884)
HORIYAMA Takashi Saitama University, Graduate School of Science and Engineering, Associate (60314530)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥11,100,000 (Direct Cost: ¥11,100,000)
Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2004: ¥4,000,000 (Direct Cost: ¥4,000,000)
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| Keywords | Discrete Algorithm / Quality for Engineering / Discrete Optimization / Network Algorithm / Enumeration Algorithm / Matching Algorithm / SAT Algorithm / Approximation Algorithm / 孤立クリーク / 最小頂点被覆問題 / マッチング / NP完全問題 |
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| Research Abstract |
Traditionally the quality of discrete algorithms has been evaluated mostly by their asymptotic running time. However, it is often pointed out that running time is not a suitable measure of quality for some applications. Recently various measures have been proposed to evaluate algorithms in many perspectives. For example, "approximation ratio" is used to evaluate approximation algorithms, where an approximation algorithm must efficiently compute reasonable solutions for hard combinatorial problems. Another example, "competitive ratio" is used to evaluate online algorithms, where in online computation an algorithm must decide how to act on incoming items of information without any knowledge of future inputs. Both measures play very important roles in current algorithm theory. In our research, we think these new measures for algorithms as "quality for engineering" and develop high performance algorithms with respect to this quality. We mainly study network algorithms, matching algorithms and satisfiability algorithms. The followings are representative results of our project.
There is an extension of stable matching problems, where ties and incomplete lists are allowed in preference lists. Finding maximum stable matchings in this setting is known to be NP-hard and (trivial) 2-approximation algorithm is also known. We show a 1.8-approximating algorithm for the problem, which first achieves the approximation ratio below 2 and improves the previous best ratio of 2-c/$\sqrt{n}$.
It is an important open question whether minimum vertex cover problems (VC) are approximable within 2-ε and it is widely believed that the answer is in the negative. We consider VC on dense graphs and show a 2 /(1+A/d) approximation algorithm, which greatly improves the ratio 2 for general graphs. Here A, (d) is a maximum (average, resp.) degree of an input graph. The result is tight in the sense that if an improvement is possible, then we would have 2-approximation algorithms for general graphs.
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