课题基金 / 基金详情

Combinatorial Methods for Discrete Geometry

Combinatorial Methods for Discrete Geometry
离散几何的组合方法
批准号:
10304008
负责人:
SAITO Akira
金额:
$17.02万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (A).
财政年份:
1998
资助国家:
日本
项目状态:
已结题
起止时间:
1998 至 2000

项目摘要

项目成果

SAITO Akira的其他基金

相似基金

相关文献

中文摘要
翻译
In this project,我们首先extracted the combinatorial aspects from a number of problems in discrete geometry,和分类他们。Then by invetigating each category,我们tried to establish general methods which are applicable to discrete geometry. The following aresome of the most successful results in this project. in discrete geometry,there are a number of problems which are essentially equivalent to joining points by straight linesegments so that the resulting geometric object becomes a hamiltonian cycle embedded in the plane这是line segments的第一个数字,我们提倡他们就是组合problems in essence,我们提倡独立的问题,我们提倡的combinatorial方法geometric trees可以handled as an extension of independent trees in graphs,我们establlished a graph-theoretic approach to address these problems. In discrete geomtery,there are many problems on dividing an Euclidean space with a finite number of geometric objects bya hyperplane so that both divided half-spaces contain almost the same number of the objects. Westudied the combinatorial aspects of these problems在其中每个对象都是一个球的问题,我们提供了许多问题discrete geometry which are essentially graph decomposition problems.我们解决了一个数字decomposition problems,especially in case of complete graphs and complete bipartite graphs. the above results are just asmall fraction of our entire resultswhich are described fully in the project report. Considering the quantity of the quality of the结果,我们believe that this project是extremely successful。
英文摘要
In this project, we first extracted the combinatorial aspects from a number of problems in discrete geometry, and categorized them. Then by invetigating each category, we tried to establish general methods which are applicable to discrete geometry. The following are some of the most successful results in this project.・ In discrete geometry, there are a number of problems which are essentially equivalent to joining points by straight line segments so that the resulting geometric object becomes a hamiltonian cycle embedded in the plane and that it has the least number of crossing of line segments. We proved that they are combinatorial problems in essence, and established a combinatorial method to tackle them.・ We proved that the problems of independent geometric trees can be handled as an extension of independent trees in graphs, and we establlished a graph-theoretic approach to address these problems.・ In discrete geomtery, there are many problems on dividing an Euclidean space with a finite number of geometric objects by a hyperplane so that both divided half-spaces contain almost the same number of the objects. We studied the combinatorial aspects of these problems, and solved the problem in which each object is a ball.・ We proved that there are many problems in discrete geometry which are essentially graph decomposition problems. We solved a number of these decomposition problems, especially in case of complete graphs and complete bipartite graphs.The above results are just a small fraction of our entire results, which are described fully in the project report. Considering the quantity of the quality of the result, we believe that this project was extremely successful.
期刊论文(235)
专著(0)
科研奖励(0)
会议论文
K.Hayase and H.Imai: "OBDDs of a Monotone Function and of Its Prime Implicants"Theory of Computing Systems. 31. 579-591 (1998)
K.Hayase 和 H.Imai:“单调函数的 OBDD 及其素蕴涵”计算系统理论。
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
Mamoru Watanabe: "Cycle reversals in oriented plane quadrangulations and orthogonal plane partitions"J.Geometry. 68. 200-208 (2000)
Mamoru Watanabe:“定向平面四边形和正交平面分割中的循环反转”J.Geometry。
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
Seiya Negami: "5-Connected planar triangulations quadrangulating other surfaces"Yokohama Math.J.. 47. 187-193 (2000)
Seiya Negami:“5-连接平面三角剖分其他曲面的四边形剖分”Yokohama Math.J.. 47. 187-193 (2000)
DOI: --
发表时间:
期刊:
影响因子: --
作者: []
通讯作者:
共 184 条
    Discovery of new graph invariants to capture the cycle ctructure
    • 批准号:
      20K11684
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.75万
    • 财政年份:
      2020
    • 负责人:
      SAITO Akira
    • 依托单位:
    Development of Novel Transmissive Light-Diffusing Material based on the Control of Disorder
    • 批准号:
      19K22062
    • 项目类别:
      Grant-in-Aid for Challenging Research (Exploratory)
    • 资助金额:
      $4.08万
    • 财政年份:
      2019
    • 负责人:
      SAITO Akira
    • 依托单位:
    Hamiltonicity of graphs and its complexity
    • 批准号:
      17K00018
    • 项目类别:
      Grant-in-Aid for Scientific Research (C)
    • 资助金额:
      $2.91万
    • 财政年份:
      2017
    • 负责人:
      SAITO Akira
    • 依托单位:
    asymmetric C-C bond formation via simultaneous activation by bimetallic catalysts
    • 批准号:
      16K18857
    • 项目类别:
      Grant-in-Aid for Young Scientists (B)
    • 资助金额:
      $2.33万
    • 财政年份:
      2016
    • 负责人:
      SAITO Akira
    • 依托单位:
    海外基金