| Project/Area Number |
10205222
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | Chuo University |
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Principal Investigator |
ASANO Takao Chuo University, Professor, 理工学部, 教授 (90124544)
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| Co-Investigator(Kenkyū-buntansha) |
UNO Takeaki NII, Associate Professor, 基礎分野, 助教授 (00302977)
MATSUI Tomomi University of Tokyo, Associate Professor, 工学研究科, 助教授 (30270888)
TSUKIYAMA Shuji Chuo University, Professor, 理工学部, 教授 (90142314)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥7,700,000 (Direct Cost: ¥7,700,000)
Fiscal Year 2000: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1999: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥3,000,000 (Direct Cost: ¥3,000,000)
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| Keywords | Approximation algorithms / Semidefinite programming / Network flow / Combinatorial optimization / Maximum satisfiability / Graph algorithms / Minimum set cover / Maximum independent set / 近似率 / VLSI設計 / MAX SAT(最大充足化問題) / MAX CUT(最大カット問題) / ネットワークフロー設計 / 列挙アルゴリズム / 近似性能 / 最適化 / 計算量 |
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| Research Abstract |
The objective of this research is to do research on approximation algorithms with high quality and high performance for combinatorial optimization problems based on network flow and semidefinite programming and contribute to the development of approximation algorithms from both theoretical and practical points of view. More specifically, we consider network problems and geometric problems including maximum satisfiability, maximum independent set, minimum set cover, VLSI physical design and so on, and obtain approximation algorithms with better performance based on network flow and semidefinite programming or on a newly proposed method. To achieve this objective, we have done the following researches.
We made an investigation on important techniques developed for designing approximation algorithms which are of high qaulity and of high performance in the fields of computational geometry, graph-network algorithms, combinatorial optimization, parallel and distributed algorithms and so on. Especially based on the semidefinte programming and network-flow techniques, we made an investigation on discrete algorithms with high performance by exchanging ideas with leading researchers in the world. Through this investigation, we could propose approximation algorithms with high qaulity and high performance in the fields of VLSI design, information networks and real world applications. Specifically, for the maximum satisfiability problem, we proposed a new algorithm with the world best record in the performance. We also implemented the algorithms as well as algorithms previously proposed by other researchers with the helps of students and made computational experiments in order to evaluate the new algorithms not only from the theoretical point of view but also from the practical point of view. The results in this research were published in the world leading journals and symposia.
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