| Project/Area Number |
10205224
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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 | Nihon University |
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Principal Investigator |
TODA Seinosuke Nihon University, Dept. of Computer Science and System Analysis, Professor, 文理学部, 教授 (90172163)
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| Co-Investigator(Kenkyū-buntansha) |
TANI Sei'ichi Nihon University, Dept. of Computer Science and System Analysis, Associate Professor, 文理学部, 助教授 (70266708)
SAITO Akira Nihon University, Dept. of Computer Science and System Analysis, Professor, 文理学部, 教授 (90186924)
YAKU Takeo Nihon University, Dept. of Computer Science and System Analysis, Professor, 文理学部, 教授 (90102821)
CHEN Zhi-zhong Tokyo Denki University, Dept. Mathematical Science, Associate Professor, 理工学部, 助教授 (00242933)
WATANABE Osamu Tokyo Institute of Technology, Dept. of Computer Science, Professor, 情報理工学研究科, 教授 (80158617)
黒田 耕嗣 日本大学, 文理学部, 教授 (50153416)
上原 隆平 駒澤大学, 自然科学教室, 講師 (00256471)
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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 |
¥10,900,000 (Direct Cost: ¥10,900,000)
Fiscal Year 2000: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1999: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1998: ¥4,600,000 (Direct Cost: ¥4,600,000)
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| Keywords | algorithm engineering / computational complexity / graph theory / isomorphism problem / isomorphism counting / tree width / Jones polynomial / graph grammar / 計算量理論 / 独立点集合問題 / 同型性判定 / 全域木 / マッチング / 二分決定グラフ / アルゴリズム / 辺連結度 / 完全独立全域木 / サイクル被覆 / 独立点集合 / 木幅 / 連結性判定問題 / 到達可能性判定問題 / グラフ認識問題 / グラフ同型性判定問題 |
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| Research Abstract |
The purpose of our research project is to analyze the computational complexity of several graph-theoretic problems, mainly in case that those input graphs are bounded on some width parameters. We investigate the following problems : (1) counting graph isomorphisms, (2) graph reachability, (3) extracting k-edge connected subgraphs, (4) deciding whether some plane graph has a dual euler tour, (5) graph decomposition, (6) applications of graph grammars to block diagrams, (7) deciding the maximum degree of a Jones polynomial, (8) random sampling and random generation. In this research project, we design many algorithms for the above problems. What we developed are : a polynomial-time algorithm for counting graph isomorphisms when those input graphs are of bounded tree-width, a logarithmic-space algorithm for graph reachability when those input graphs are of bounded path-width, a polynomial-time approximation scheme for. extracting k-edge subgraphs, a linear-time algorithm for deciding whether a given plane graph has a dual euler tour, a polynomial-time algorithm for computing the maximum degree of Jones polynomial of some class of pretzel links, design a graph grammar for manipulating block diagrams and an efficient algorithm for those syntactic analysis, an efficient random algorithm for generating uniformly an input data for SAT/MAXSAT problem.
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