A Differential Geometric Research on the Construction of Highly Connected Graphs Applicable to Big Data Analysis

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K23411
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Shimane University (2020-2021); Research Institute for Humanity and Nature (2019)
• Principal Investigator: Yamada Taiki 島根大学, 学術研究院理工学系, 助教 (00847270)
• Project Period (FY): 2019-08-30 – 2022-03-31
• Keywords: グラフ理論 / リッチ曲率 / 連結度

Outline of Final Research Achievements

The purpose of this research is to establish a differential geometrical method that can construct graphs that strengthen graph connectivity, an invariant that indicates the strength of graph ties, and we challenge the pioneering theory of constructing new algorithms.
The connectivity of graphs has been widely applied to real-world problems such as fault-tolerant network design problems, but recently, with the development of big data, it has become necessary to deal with larger graphs. In Riemannian geometry, we focused on Ricci curvature, which can obtain the structure of manifolds from local calculations.
The results of this research have been summarized in three papers, all of which have been published in international journals.

Free Research Field

離散幾何学

Academic Significance and Societal Importance of the Research Achievements

本研究は，申請者の構築した有向グラフ上の理論やコホモロジー論を用いることで，微分幾何学の概念であるリッチ曲率と組合せ論の概念である連結度を結びつける接合的研究に位置付けられるため，双方の学問分野において波及効果を及ぼす.また，ビッグデータの整備が進んでいる昨今において，効率的な解析手法を提案する本研究は学術領域だけでなく，実社会にも大きなインパクトを与える.