Graph realization problem and graph rigidity

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K15942
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: The University of Tokyo (2017-2018); Kyoto University (2015-2016)
• Principal Investigator: Tanigawa Shinichi 東京大学, 大学院情報理工学系研究科, 准教授 (30623540)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: グラフの実現問題 / グラフ剛性 / 半正定値計画問題

Outline of Final Research Achievements

Understanding the facial structure of projections of the elliptopes is a fundamental question in convex optimization. In this study we showed a new connection between projections of the elliptopes and the classical distance polyhedra. Based on this connection, we developed a new combinatorial algorithm for the graph realization problem.
We also obtain a substantial contribution to graph rigidity theory. Among others we affirmatively settled a conjecture by Whiteley concerning the global rigidity of simplicial polytopes.

Free Research Field

離散最適化

Academic Significance and Societal Importance of the Research Achievements

グラフを入力とする連続最適化問題は、情報科学の様々な場面で見られる話題であり、入力の疎性を利用した高速アルゴリズムの設計は一般的に広く利用される技術である。本研究はグラフの実現問題に対し、入力グラフの代数的・幾何的性質を利用することで、さらに高度で独創的な解法の提案に成功した。