Development and Evaluations of Efficient Algorithms for Finding a Maximum Clique Based upon Nueral Networks
| Project/Area Number |
02650261
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
情報工学
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| Research Institution | The Univesity of Electro-Communications |
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Principal Investigator |
TOMITA Etsuji The University of Electro-Communications Dept. of Communications and Systems, Professor, 電気通信学部, 教授 (40016598)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOMORI Takashi The University of Electro-Communications Dept. of Computer Science and Informati, 電気通信学部, 助教授 (60139722)
TAKEDA Mitsuo The University of Electro-Communications Dept. of Communications and Systems, Pr, 電気通信学部, 教授 (00114926)
TAKAHASHI Haruhisa The University of Electro-Communications Dept. of Communications and Systems, As, 電気通信学部, 助教授 (90135418)
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| Project Period (FY) |
1990 – 1991
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| Project Status |
Completed (Fiscal Year 1991)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1991: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1990: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Neural network / Graph / Clique / Boltzmann machine / Randamized algorithm / N-queen problem / 近似アルゴリズム / アルゴリズム / nークィ-ン問題 |
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| Research Abstract |
1. Given a graph of n nodes, we have devised an 0(n^3)-time algorithm NMCLIQ for finding a near-maximum clique. We have confirmed in experiments for several graphs with up to 400 nodes that the orders of maximal c)iques found by NMCLIQ are almost more than 85% of the maximum orders.
2. We have developed an 0(n^3)-time algorithm RACLIQUE for finding a near-maximum clique in a given graph of n nodes. While the algorithm is based upon the notion of Boltzmann machines, it employs no simulated annealing and hence is simple to control its execution. We have confirmed in experiments for several random and nonrandom graphs with up to 400 nodes that almost optimum solutions can be found very efficiently. In addition, further improvements and variations are considered and verified to be very useful.
3. We have devised two non-searching algorithms for the n-queen problem which are based upon the former resuit for finding a near-maximum clique. We have confirmed in experiments for up to 50, 000 queens that they are extremly efficient.
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Report
(3 results)
Research Products
(30 results)
