2006 Fiscal Year Final Research Report Summary
Studies on Diarete Algorithms with Guaranteed Quality based on Engineering Criteria
| 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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| Keywords | Discrete Algorithm / Quality for Engineering / Discrete Optimization / Network Algorithm / Enumeration Algorithm / Matching Algorithm / SAT Algorithm / Approximation Algorithm |
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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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Research Products
(106 results)
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[Journal Article] Quantum Lower Bounds for the Goldreich-Levin Problem2006
Author(s)
M., Adcock, It, Cleve, K., Iwama, R., Raymond, S., Yamashita
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Journal Title
Information Processing Letters vol.97, no. 5
Pages: 208-211
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] (4,1)-Quantum Random Access Coding does not Exist - One Qubit is not Enough to Recover One of Four Bits2006
Author(s)
M., Hayashi, K., Iwama, H., Nishimura, R., Raymond, S., Yamashita
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Journal Title
New Journal of Physics vol.18, no. 129
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] How to Collect Balls Moving in the Euclidean Plane2006
Author(s)
Y., Asahiro, T., Horiyama, K., Makino, H., Ono, T., Sakuma, M., Yamashita
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Journal Title
Discrete Applied Mathematics vol.154/16
Pages: 2247-2262
Description
「研究成果報告書概要(欧文)」より
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[Journal Article] C_7-coloring problem2004
Author(s)
A., Uejima, H., Ito, T., Tsukiji
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Journal Title
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences vol.87, no. 5
Pages: 1243-1250
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Quantum Network Coding2007
Author(s)
M. Hayashi, K. Iwama, H. Nishimura, R. Raymond, S. Yamashita
Organizer
24th International Symposium on Theoretical Aspects of Computer Science(STACS 2007)
Place of Presentation
Aachen, Germany
Year and Date
20070200
Description
「研究成果報告書概要(和文)」より
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[Presentation] Quantum Network Coding2007
Author(s)
M., Hayashi, K., Iwama, H., Nishimura, R., Raymond, S., Yamashita
Organizer
24th International Symposium on Theoretical Aspects of Computer Science (STAGS 2007)
Place of Presentation
Germany
Year and Date
20070200
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Harmonic Algorithm for 3-Dimensional Strip Packing Problem2007
Author(s)
N., Bansal, X., Han, K., Iwama, M., Sviridenko, G., Zhang
Organizer
18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2007)
Place of Presentation
Louisiana, USA
Year and Date
20070100
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Improved Algorithms for Quantum Identification of Boolean Oracles2006
Author(s)
A., Ambainis, K., Iwama, A., Kawacbi, It, Raymond, S., Yamashita
Organizer
10th Scandinavian Workshop on Algorithm Theory (SWAT 2006)
Place of Presentation
Riga, Latvia
Year and Date
20060700
Description
「研究成果報告書概要(欧文)」より
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[Presentation] (4,1)-Quantum Random Access Coding Does Not Exist2006
Author(s)
M., Hayashi, K., Iwama, H., Nishimura, R., Raymond, S., Yamashita
Organizer
IEEE International Symposium on Information Theory (ISIT 2006)
Place of Presentation
Washington, USA
Year and Date
20060700
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Quantum Network Coding2006
Author(s)
M. Hayashi, K. Iwama, H. Nishimura, R. Raymond, S. Yamashita
Organizer
The 9th Workshop on Quantum Information Processing(QIP2006)
Place of Presentation
Paris. Framce
Year and Date
20060100
Description
「研究成果報告書概要(和文)」より
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[Presentation] Quantum Network Coding2006
Author(s)
M., Hayashi, K., Iwama, H., Nishimura, R., Raymond, S., Yamashita
Organizer
Proc. the 9th Workshop on Quantum Information Processing (QIP2006)
Place of Presentation
Paris. Framce
Year and Date
20060100
Description
「研究成果報告書概要(欧文)」より
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[Presentation] On-line Removable Square Packing2005
Author(s)
X. Han, K. Iwama, G. Zhang
Organizer
3rd International Workshop on Approximation and Online Algorithms(WAOA 2005)
Place of Presentation
Palma de Mallorca, Spain
Year and Date
20051000
Description
「研究成果報告書概要(和文)」より
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[Presentation] On-line Removable Square Packing2005
Author(s)
X., Han, K., Iwama, G., Zhang
Organizer
The 3rd International Workshop on Approximation and Online Algorithms (WAOA 2005)
Place of Presentation
Spain
Year and Date
20051000
Description
「研究成果報告書概要(欧文)」より
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[Presentation] The Delayed k-Server Problem2005
Author(s)
W. W. Bein, K. Iwama, L. L. Larmore, J. Noga
Organizer
The 15th International Symposium on Fundamentals of Computation Theory(FCT 2005)
Place of Presentation
Luebeck, Germany
Year and Date
20050800
Description
「研究成果報告書概要(和文)」より
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[Presentation] The Delayed k-Server Problem2005
Author(s)
W., W., Bein, K., Iwama, L., L., Larmore, J., Noga
Organizer
15th International Symposium on Fundamentals of Computation Theory (FCT 2005)
Place of Presentation
Luebeck, Germany
Year and Date
20050800
Description
「研究成果報告書概要(欧文)」より
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[Presentation] Hajos Calculus on Planar Graphs2005
Author(s)
Y. Hanatani, T. Horiyama, K. Iwama
Organizer
The 4th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
Place of Presentation
Hungary
Year and Date
20050100
Description
「研究成果報告書概要(和文)」より
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[Presentation] Robust Quantum Algorithms for Oracle Indentification2005
Author(s)
K., Iwama, A., Kawachi, Rudy, Raymond, H., P., S., Yamashita
Organizer
8th workshop on Quantum Information Processing (QIP 2005)
Place of Presentation
Massachusetts, USA
Year and Date
20050100
Description
「研究成果報告書概要(欧文)」より
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