Research on dynamic geometric problems and computational topological algorithms

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K00024
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Chuo University
• Principal Investigator: IMAI Keiko 中央大学, 理工学部, 教授 (70203289)
• Co-Investigator(Kenkyū-buntansha): 森口 昌樹 中央大学, 理工学部, 准教授 (10525893)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 計算幾何学 / 計算位相幾何学 / 動的ラベル配置 / 路線図自動生成 / 錯視立体

Outline of Final Research Achievements

We have been investigated algorithms and data structures in Computational Geometry and Computational Topology. In the geographic information systems, a large amount of geometric data has to be handled, and there are many problems that must be solved in real time as the map is zoomed in and out and we also considered problems in a dynamic environment where the object is moving. We formulated some of these problems as optimization problems and proposed solution methods. Mainly, in this project, we considered label placement problems, in particular, we proposed polynomial time algorithms for label size maximization on rotating maps and approximation algorithms for minimum point-overlap labeling. We gave solutions in automatic drawing problems for metro maps. Also we studied Reeb graphs of geometric objects and optical illusion 3D solids. The results of our research were presented at international conferences and research meetings, and published in academic journals.

Free Research Field

数理工学

Academic Significance and Societal Importance of the Research Achievements

本研究では大量の幾何情報を効率よく扱うためのアルゴリズムやデータ構造を研究する分野である計算幾何学と，物体の構造を表現する位相構造をコンピュータで扱う分野である計算位相幾何学における問題を研究してきた．特に，地理情報システムにおいてはモバイル端末で地図を扱うことが一般的となり，動的なデータ処理を効率的に行わなければならない場面が多くなっている．3次元物体はデータ量が多く，構造を抽出してデータを削減する必要もある．理論的な問題の定式化手法や解法を提案しているという点，現実的な問題を解決することを念頭に幾何学的データを処理する問題の解法を与えていることから，学術的意義，社会的意義があると考える．