Project/Area Number  08680377 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
計算機科学

Research Institution  KYOTO UNIVERSITY 
Principal Investigator 
KATOH Naoki Kyoto University, Graduate School of EngineerinDepartment of Architecture and Architectural Systems, Professor, 工学研究科, 教授 (40145826)

CoInvestigator(Kenkyūbuntansha) 
YANG Dai Tokyo Institute of Technology, Graduate School of Information Scinece and Engine, 大学院・情報理工学研究科, 講師 (40244678)
OHSAKI Makoto Kyoto University, Graduate School of Engineering, Department of Architecture and, 工学研究科, 助教授 (40176855)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1997 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1996 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  triangulation / computational geometry / algorithm / branch and bound / structural optimization / topology optimization / 3角形分割 / 計算幾何学 / アルゴリズム / 分枝限定法 / 構造最適化 / トポロジー最適化 / 三角形分割 / LMTSkeleton / 組合せ最適 / 動的計画法 / 最小重みマッチング 
Research Abstract 
Over the last two yeras, we have tried to develop an efficient exact algorithm for computing a minimum weight triangulation (MWT for short) for points in the plane. For this purpose we have first developed a new way to compute an effective lower bound on the length of MWT,based on the miniumu weight matching of a graph appropriately defined for arbitrary two triangulations. We have verified by computational experimetns that the proposed lower bound is very close to the optimal. We also developed an 0 (n^3logn) algorithm for computing an LMTskeleton which is subgraph of MWT.We have carried out computational experiments for randomly generated point sets in order to see how large LMTskeletons are. The results demonstrated that for most cases LMTskeleton becomes connected, implying that MWT can be computed efficiently in a practical sense. Combining these tow ideas, we then developed a branch and bound algorithm for computing MWT.We have applied our algorithm to several hard instances whose LMTskeletons are highly disconnected. Computational results showed that the proposed algorithm can compute MWT for such hard instances. We also considered a problem of computing MWT with angular constrants such that maximum and/or minimum angles are less than (resp.larger than) or equal to a given threshold. We have developed an algorithm for computing LMTskeletons for such constrained MWT. Finally, we formulated structural optimization problems we encounter in architecture as a variant of MWT problems. In particular, we considered a problem of finding and optimal topology and node positions of triangular trusses under the constraint concerning strudtural characteristics.
