Theoretical Foundation of Innovative Data Analysis Based on Computational Geometry and Topology

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K00009
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Okamoto Yoshio 電気通信大学, 大学院情報理工学研究科, 教授 (00402660)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 計算幾何学 / 離散数学 / アルゴリズム理論

Outline of Final Research Achievements

Below is the summary of representative results from this project.
(1) Efficient algorithms have been developed for computing the diameter and the radius of a bounded polygonal domain. (2) Prescription of edge lengths has been studied for graphs embedded on the plane by straight line segments without edge crossings. (3) Restrictions of edge crossing patterns and curve types have been studied for graphs embedded on the plane. (4) Recursive decomposition data structures have been proposed for unit disk graphs that have been used for modeling sensor networks in the literature.

Free Research Field

情報学基礎理論

Academic Significance and Societal Importance of the Research Achievements

計算幾何学，計算トポロジーは情報学基礎理論における比較的若い研究分野であるが，それであっても，多くの問題が未解決のまま残されている．現在，幾何的データやトポロジー的データは世の中に満ち溢れ，それらの処理に対して，計算幾何学と計算トポロジーの果たす役割は今後一層増していくことが予想される．そのような未来に対して，本研究の培った技法や知見が基盤的な位置づけを担うこととなる．