2006 Fiscal Year Final Research Report Summary
Developments of Efficient Combinatorial Algorithms and Their Applications
| Project/Area Number |
16300001
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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 | The University of Electro-Communications |
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Principal Investigator |
TOMITA Etsuji The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (40016598)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Haruhisa Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (90135418)
NISHINO Tetsuro Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (10198484)
KOBAYASHI Satoshi Faculty of Electro-Communications, Associate Professor, 電気通信学部, 助教授 (50251707)
HOTTA Kazuhiro Faculty of Electro-Communications, Research Associate, 電気通信学部, 助手 (40345426)
WAKATSUKI Mitsuo Faculty of Electro-Communications, Research Associate, 電気通信学部, 助手 (30251705)
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| Project Period (FY) |
2004 – 2006
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| Keywords | maximum clique / maximal clique / branch-and-bound method / approximate coloring / generation / bioinformatics / algorithmic learning theory / learning from positive data |
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| Research Abstract |
(1)We are mainly concerned with the maximum clique problem that is very important and is one of the most typical NP hard combinatorial problems. We employed a branch-and-bound algorithm for the problem and established an efficient ordering of vertices to search them. In addition, we developed a new approximate coloring algorithm to give an upper bound of the size of a maximum clique in question in order to bound the search. By combining these techniques, we developed very efficient algorithms for finding a maximum clique. The superiority of our algorithms over the other algorithms were confirmed by extensive computational experiments on random graphs and DIMACS benchmark graphs.
(2)We developed an algorithm for generating all the maximal cliques in a graph and proved that it is theoretically optimum and runs very fast in practice. A more efficient algorithm that generates only large maximal cliques was also developed, that is important for practical uses. In addition, efficient algorithms that generate maximal bipartite graphs in a bipartite graph was developed.
(3)These algorithms were successfully applied for practical problems in bioinformatics such as a protein side-chain packing problem and a protein threading problem.
(4)We obtained new results of algorithmic learning of simple languages via queries, learning of Boolean functions from noisy samples, learning of a certain kind of counter language from positive data, and gave a unified approach for identification in the limit from positive data.
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