1999 Fiscal Year Final Research Report Summary
Polynomial time algorithm for dualizing a monotone DNF
| Project/Area Number |
10680365
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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 | Meiji University |
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Principal Investigator |
TAMAKI Hisao Meiji University/School of Science and Technology/Professor, 理工学部, 教授 (20111354)
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| Project Period (FY) |
1998 – 1999
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| Keywords | monotone DNF / duality / dualization / hypergraph / minimal transversal / polynomial time / space efficiency |
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| Research Abstract |
The goal of this research project was to develop an algorithm for dualizing a boolean function given in DNF, that runs in time polynomial in the total size of the input and output. This problem is equivalent to the problem of generating all the minimal transversals of a given hypergraph. We were unable to achieve this ultimate goal. However, we discovered an algorithm for generating all the minimal transversals of a hypergraph using O (n log n) words of storage, where n is the size of the input hypergraph. The time complexity of this algorithm is quasi-polynomial and almost the same as the best known algorithm due to Fredman and Khachiyan. We have also discovered a polynomial time delay algorithm for generating all the minimal transversals of a given bounded-degree hypergraph.
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