Establishing the foundation of discrete mathematics in the field of architecture and urban planning and its application to large-scale optimization

2016 Fiscal Year Final Research Report

• Project/Area Number: 25240004
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Kwansei Gakuin University (2016); Kyoto University (2013-2015)
• Principal Investigator: Katoh Naoki 関西学院大学, 理工学部, 教授 (40145826)
• Co-Investigator(Kenkyū-buntansha): 神山 直之 九州大学, マス・フォア・インダストリ研究所, 准教授 (10548134) ; 谷川 眞一 京都大学, 数理解析研究所, 助教 (30623540) ; 藤澤 克樹 九州大学, マス・フォア・インダストリ研究所, 教授 (40303854) ; 瀧澤 重志 大阪市立大学, 大学院工学研究科, 准教授 (40304133) ; 伊藤 仁一 熊本大学, 教育学部, 教授 (20193493) ; 東川 雄哉 中央大学, 理工学部, 助教 (20749486) ; 小林 祐貴 東京工業大学, 環境・社会理工学院, 助教 (70756668) ; 山川 誠 東京電機大学, 公私立大学の部局等, 准教授 (50378816)
• Co-Investigator(Renkei-kenkyūsha): MINATO Shin-ichi 北海道大学, 情報科学研究科, 教授 (10374612) ; UNO Takeaki 国立情報学研究所, 情報学プリンシプル研究系, 教授 (00302977)
• Research Collaborator: SUZUMURA Toyotaro 米国 IBM, ワトソン研究所, Research Staff Member
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 最速フロー / 組合せ剛性理論 / 大域剛性 / 避難計画 / ブレース追加問題 / 普遍的最速フロー / 冗長剛性

Outline of Final Research Achievements

In this project, we have obtained the following results.
1. In an emergent evacuation planning model based on dynamic flow model, the effectiveness of evacuation by a lexicographically quickest flow was demonstrated. 2. Assuming the situation that Umeda underground mall is inundated due to tsunami and/or flood, we carried out a multi-agent simulation of vertical evacuation to connected buildings to compute the evacuation completion time and to obtain the knowledge of crowded areas. 3. We proposed an algorithm for a quickest transshipment problem that models an emergent situation in which people can evacuate on foot or by car. 4. We derived a combinatorial characterization of global rigidity of body-hinge frameworks. 5. We characterized the redundant rigidity and the redundant global rigidity of body-hinge graphs in terms of graph connectivity.6. We presented an algorithm for adding braces to a square grid framework possibly with holes in order to make the framework minimally rigid.

Free Research Field

離散アルゴリズム