2017 Fiscal Year Final Research Report
Enumeration of geometric figures and its application
| Project/Area Number |
15K00008
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | Saitama University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | アルゴリズム / 列挙アルゴリズム / 計算幾何学 / 展開図 / 多面体 / 選挙区割り |
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| Outline of Final Research Achievements |
The methodology for designing enumeration algorithms of geometric objects are discussed by integrating basic technologies (e.g., BDDs (Binary Decision Diagrams), ZDDs (Zero-suppressed BDDs) and reverse search). We also applied the methodology to various fields. First, we focused on enumerating the developments of orthogonal boxes. We introduced the notion of unit square development, and proposed an efficient algorithms for constructing ZDDs of the unit square developments. We also considered the problem from the reverse side. That is, we proposed algorithms checking whether a given orthogonal polygon can be folded into an orthogonal box (and giving the creases if possible). As for the application of our method, we have enumerated all patterns of partitions for elections within a disparity bound, and also all rhombille tilings.
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| Free Research Field |
計算幾何学
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