1997 Fiscal Year Final Research Report Summary
Development of an Exact Algorithm for Computing Minimum Weight Triangulations
| Project/Area Number |
08680377
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | KYOTO UNIVERSITY (1997)
Kobe University of Commerce (1996) |
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Principal Investigator |
KATOH Naoki Kyoto University, Graduate School of EngineerinDepartment of Architecture and Architectural Systems, Professor, 工学研究科, 教授 (40145826)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1996 – 1997
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| Keywords | triangulation / computational geometry / algorithm / branch and bound / structural optimization / topology optimization |
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| 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 LMT-skeleton which is subgraph of MWT.We have carried out computational experiments for randomly generated point sets in order to see how large LMT-skeletons are. The results demonstrated that for most cases LMT-skeleton 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 LMT-skeletons 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 LMT-skeletons 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.
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