| Project/Area Number |
11640105
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
ANDO Kiyoshi The University of Electro-Communications, Fucult. of Electro-Communications, Professor, 電気通信学部, 教授 (20096944)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIGAMI Yoshiyasu The University of Electro-Communications, Fucult. of Electro-Communications, Associate, 電気通信学部, 助手 (50262374)
TAMURA Akihisa Kyoto University, Fucult. of Sciences, Associate Professor, 理学部, 助教授 (50217189)
ASANO Tetsuo Japan Advanced Institute of Science and Technology, Graduate School of Information Science, Professor, 情報科学研究科, 教授 (90113133)
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| Project Period (FY) |
1999 – 2001
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| Keywords | graph thory / discrete optimization / algorithm / computational geometry / discrete geometry / combinatorial geometry / combinatorics / extremal graph theory |
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| Research Abstract |
In computational geometry, we proposed an idea of a geometric representation of an image by using contour line which enables approaches completely different from conventional ones based on matrix representation of an image. We also gave an algorithm to approximate rectilinear contour lines by smooth curves while keeping several basic properties inherent in contour lines. These applications are closely related to digital geometry in which vertices have integer coordinates. We investigated a new approach for Digital halftoning which is a technique to convert a grey image into a binary (black and white) image. We introduced an notion of bidirected graph as an extension of directed graph and we gave a linear time algorithm for the generalized stable set problem on triangulated bidirected graphs. We proposed a polynomial time algorithm for the M-convex function minimization problem. We proved that the edge wide-diameter of a k-edge connected graph does not exceed a plynomial of the diameter of it of degree k. We proved that the number of vertices of degree 5 of every 5-contraction critical graph is at least 1/5 of its order and the number of vertices of degree 6 of every 6-contraction critical graph is at least 1/7 of its order. We developed a new pseudo-probablistic method and we proved Bollbas-Kohayakawa conjecture on Erdos-Stone theorem.
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