Research on the isomorphism for the enumeration of geometric figures
| Project/Area Number |
18K11153
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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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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Hokkaido University (2019-2020)
Saitama University (2018) |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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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 / 二分決定グラフ / 逆探索法 / 包囲多角形 / タイリング |
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| Outline of Final Research Achievements |
We focused on the isomorphism, which appears in various problems of computational geometry. We developed isomorphism-elimination algorithms for enumerating geometric objects, and applied the methodology to various fields. The enumeration by our proposed algorithms are based on BDDs (Binary Decision Diagrams) and ZDDs (Zero-suppressed BDDs). By combining the algorithms with the enumeration algorithms with the frontier-method, which is the framework for constructing BDDs/ZDDs in the top-down manner, the enumeration achieves extremely fast speed and extremely small memory consumption. For example, experimental results show that the proposed method is more than 300 times faster and 3,000 times less memory than the conventional algorithm with only the frontier-method.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題で取り組んだ同型性の除去は、計算幾何学においてさまざまな問題に横断的に現れる重要な課題である。たとえば、研究代表者がこれまでに幾何図形列挙の応用として取り組んだ、選挙区の区割り問題や、避難所の割当て問題、高分子化合物のトポロジーの列挙などに現れている。こうした諸問題に対し、個別の問題に応じて「何をもって同型とするか」の定義を確認する必要がある。一方で、その先の同型性の除去については、個別に対応を考えるのではなく、それらに共通して必要となる要素を抽出し、同型性をうまく扱うためのアルゴリズム設計の基盤を構築できたことに学術的かつ社会的意義がある。
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Report
(4 results)
Research Products
(70 results)
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[Journal Article] Rigid Foldability is NP-Hard2020
Author(s)
H. A. Akitaya, E. D. Demaine, T. Horiyama, T. C. Hull, J. S. Ku, T. Tachi,
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Journal Title
Journal of Computational Geometry
Volume: 11(1)
Pages: 93-124
Related Report
Peer Reviewed / Int'l Joint Research
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[Journal Article] Sequentially Swapping Colored Tokens on Graphs2019
Author(s)
Katsuhisa Yamanaka, Erik D. Demaine, Takashi Horiyama, Akitoshi Kawamura, Shin-Ichi Nakano, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, and Takeaki Uno
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Journal Title
Journal of Graph Algorithms and Applications
Volume: 23
Issue: 1
Pages: 3-27
DOI
NAID
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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[Journal Article] Max-Min 3-Dispersion Problems2019
Author(s)
T. Horiyama, S. Nakano, T. Saitoh, K. Suetsugu, A. Suzuki, R. Uehara, T. Uno, K. Wasa
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Journal Title
Lecture Notes in Computer Science
Volume: 11653
Pages: 291-300
NAID
Related Report
Peer Reviewed
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[Journal Article] Efficient Segment Folding is Hard2019
Author(s)
T. Horiyama, F. Klute, M. Korman, I. Parada, R. Uehara, K. Yamanaka
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Journal Title
Proc. of the 31st Canadian Conference on Computational Geometry
Volume: 31
Pages: 177-183
Related Report
Peer Reviewed / Int'l Joint Research
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[Presentation] Enumerating Empty Polygons2020
Author(s)
S. Terui, T. Hirayama, T. Horiyama, K. Yamanaka, T. Uno
Organizer
The 4th International Workshop on Enumeration Problems \& Applications
Related Report
Int'l Joint Research
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