1998 Fiscal Year Final Research Report Summary
Development and Applications of Efficient Algorithms for Combinatorial Optimization Problems
| Project/Area Number |
09680331
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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 |
計算機科学
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
TOMITA Etsuji The University of Electro-Communications, Dept.of Communications and Systems Engineering, Professor, 電気通信学部, 教授 (40016598)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Haruhisa The University of Electro-Communications, Dept.of Communications and Systems Eng, 電気通信学部, 助教授 (90135418)
WAKATSUKI Mitsuo The University of Electro-Communications, Dept.of Communications and Systems Eng, 電気通信学部, 助手 (30251705)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Combinatorial optimization / Maximum clique / Maximum weight clique / Maximal clique / Coloring problem / Approximation algorithm / Dominating Set / RNA secondary structure prediction |
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| Research Abstract |
(1) We have developed branch and bound algorithm for finding a maximum clique in an undirected graph. They successfully employ greedy coloring algorithms to give the upper bounds for the size of a maximum clique. The algorithms are evaluated experimentally for not only a number of random graphs but also DIMACS bench mark graphs and have been proved very efficient. An approximation algorithm is also developed for the maximum clique problem. In addition, efficient branch and bound algorithms are developed for finding a maximum weight clique in a weighted graph. An algorithm for finding all the maximal cliques are established and proved to be very efficient in experiments.
(2) Approximate and exact algorithms are developed for the vertex coloring problem by employing the above mentioned ideas. They are confirmed to be very efficient for a number of random graphs and DIMACS bench mark graphs.
(3) As extensions of the above algorithms, efficient algorithm are developed for the Traveling Salesman Problem, and RNA Secondary Structure Problem.
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