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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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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 / 計算機科学 |
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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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Report
(4 results)
Research Products
(41 results)
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[Journal Article] Sequentially Swapping Colored Tokens on Graphs2017
Author(s)
Katsuhisa Yamanaka, Erik D. Demaine, Takashi Horiyama, Akitoshi Kawamura, Shin-Ichi Nakano, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno
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Journal Title
Proceedings of 11th International Conference and Workshop on Algorithms and Computation (WALCOM 2017)
Volume: -
Pages: 435-447
DOI
NAID
ISBN
9783319539249, 9783319539256
Related Report
Peer Reviewed / Int'l Joint Research
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[Journal Article] Box Pleating is Hard2016
Author(s)
H. Akitaya, K. C. Cheung, E. D. Demaine, T. Horiyama, T. Hull, J. S. Ku, T. Tachi, R. Uehara
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Journal Title
Lecture Notes in Computer Science
Volume: 9943
Pages: 167-179
DOI
ISBN
9783319485317, 9783319485324
Related Report
Peer Reviewed / Int'l Joint Research
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[Journal Article] Swapping Colored Tokens on Graphs2015
Author(s)
K. Yamanaka, T. Horiyama, D. Kirkpatrick, Y. Otachi, T. Saitoh, R. Uehara, Y. Uno
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Journal Title
Lecture Notes in Computer Science
Volume: 9214
Pages: 619-628
DOI
NAID
ISBN
9783319218397, 9783319218403
Related Report
Peer Reviewed / Int'l Joint Research
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[Presentation] 色付きトークン整列問題の計算複雑さ2016
Author(s)
山中克久, 堀山貴史, カークパトリック ディビッド, 大舘陽太, 斎藤寿樹, 上原隆平, 宇野裕之
Organizer
情報処理学会, アルゴリズム研究会
Place of Presentation
湯の原ホテル (宮城県仙台市)
Year and Date
2016-01-21
Related Report
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[Presentation] Continuous Folding of Regular Dodecahedra2015
Author(s)
T. Horiyama, J. Itoh, N. Katoh, Y. Kobayashi, C. Nara
Organizer
18th Japan Conference on Discrete and Computational Geometry and Graphs
Place of Presentation
京都大学吉田キャンパス (京都府京都市)
Year and Date
2015-09-16
Related Report
Int'l Joint Research
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[Presentation] Box Pleating is Hard2015
Author(s)
J. S. Ku, H. Akitaya, E. D. Demaine, T. Hull, K. C. Cheung, T. Horiyama, T. Tachi, R. Uehara
Organizer
18th Japan Conference on Discrete and Computational Geometry and Graphs
Place of Presentation
京都大学吉田キャンパス (京都府京都市)
Year and Date
2015-09-16
Related Report
Int'l Joint Research
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[Presentation] Ls in L and Sphinxes in Sphinx2015
Author(s)
T. Horiyama, Y. Okamoto, R. Uehara
Organizer
18th Korea-Japan Joint Workshop on Algorithms and Computation
Place of Presentation
Songdo Convensia, Incheon, Korea
Year and Date
2015-08-22
Related Report
Int'l Joint Research
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