Theoretical Foundation of Innovative Data Analysis Based on Computational Geometry and Topology

• Project/Area Number: 15K00009
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Okamoto Yoshio 電気通信大学, 大学院情報理工学研究科, 教授 (00402660)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Project Status: Completed (Fiscal Year 2018)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 計算幾何学 / 離散数学 / アルゴリズム理論 / 離散幾何学

Outline of Final Research Achievements

Below is the summary of representative results from this project.
(1) Efficient algorithms have been developed for computing the diameter and the radius of a bounded polygonal domain. (2) Prescription of edge lengths has been studied for graphs embedded on the plane by straight line segments without edge crossings. (3) Restrictions of edge crossing patterns and curve types have been studied for graphs embedded on the plane. (4) Recursive decomposition data structures have been proposed for unit disk graphs that have been used for modeling sensor networks in the literature.

Academic Significance and Societal Importance of the Research Achievements

計算幾何学，計算トポロジーは情報学基礎理論における比較的若い研究分野であるが，それであっても，多くの問題が未解決のまま残されている．現在，幾何的データやトポロジー的データは世の中に満ち溢れ，それらの処理に対して，計算幾何学と計算トポロジーの果たす役割は今後一層増していくことが予想される．そのような未来に対して，本研究の培った技法や知見が基盤的な位置づけを担うこととなる．

Research Products

• [Int'l Joint Research] サンクトペテルブルク大学(ロシア連邦)
• [Int'l Joint Research] ブリュッセル自由大学(ベルギー)
• [Int'l Joint Research] ベルリン自由大学/チュービンゲン大学/ヴュルツブルク大学(ドイツ)
• [Int'l Joint Research] タフツ大学(米国)
• [Int'l Joint Research] シドニー大学(オーストラリア)
• [Int'l Joint Research]
• [Int'l Joint Research] ネゲヴ・ベン＝グリオン大学(イスラエル)
• [Int'l Joint Research] アイントホーフェン工科大学(オランダ)
• [Int'l Joint Research] ブリュッセル自由大学(ベルギー)
• [Int'l Joint Research] 京義大学校(韓国)
• [Int'l Joint Research] ニューヨーク州立大学ストーニーブルック校/ユタ州立大学/マサチューセッツ工科大学(米国)
• [Int'l Joint Research] リンショーピング大学(スウェーデン)
• [Int'l Joint Research] ベルリン自由大学/ザールランド大学(ドイツ)
• [Int'l Joint Research] スイス連邦工科大学チューリヒ校(スイス)
• [Int'l Joint Research]
• [Journal Article] Exact Algorithms for the Max-Min Dispersion Problem (2018)
  • Author(s): Toshihiro Akagi, Tetsuya Araki, Takashi Horiyama, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara, Takeaki Uno, Kunihiro Wasa
  • Journal Title: Proceedings of 12th International Frontiers of Algorithmics Workshop (FAW 2018) Volume: --- Pages: 263-272
  • DOI: 10.1007/978-3-319-78455-7_20
  • NAID: 120006648104
  • ISBN: 9783319784540, 9783319784557
  • Peer Reviewed
• [Journal Article] Computational Complexity of Robot Arm Simulation Problems (2018)
  • Author(s): Feng Tianfeng、Horiyama Takashi、Okamoto Yoshio、Otachi Yota、Saitoh Toshiki、Uno Takeaki、Uehara Ryuhei
  • Journal Title: Lecture Notes in Computer Science Volume: 10979 Pages: 177-188
  • DOI: 10.1007/978-3-319-94667-2_15
  • ISBN: 9783319946665, 9783319946672
  • Peer Reviewed
• [Journal Article] Orthogonal and Smooth Orthogonal Layouts of 1-Planar Graphs with Low Edge Complexity (2018)
  • Author(s): Evmorfia Argyriou, Sabine Cornelsen, Henry Forster, Michael Kaufmann, Martin Nollenburg, Yoshio Okamoto, Chrysanthi Raftopoulou, and Alexander Wolff
  • Journal Title: Proceedings of 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) Volume: --- Pages: 509-523
  • DOI: 10.1007/978-3-030-04414-5_36
  • ISBN: 9783030044138, 9783030044145
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain (2018)
  • Author(s): Elena Arseneva, Man-Kwun Chiu, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurelien Ooms, Andre van Renssen, Marcel Roeloffzen
  • Journal Title: Proceedings of 29th International Symposium on Algorithms and Computation (ISAAC 2018) Volume: ---
  • DOI: 10.4230/LIPICS.ISAAC.2018.58
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Tight approximability of the server allocation problem for real-time applications (2018)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto, and Taichi Shiitada
  • Journal Title: Proceedings of 3rd International Workshop on Algorithmic Aspects of Cloud Computing (ALGOCLOUD 2017) Volume: --- Pages: 41-55
  • DOI: 10.1007/978-3-319-74875-7_4
  • NAID: 120006998850
  • ISBN: 9783319748740, 9783319748757
  • Peer Reviewed / Open Access
• [Journal Article] General constructions of rational secret sharing with expected constant-round reconstruction (2017)
  • Author(s): Akinori Kawachi, Yoshio Okamoto, Keisuke Tanaka, and Kenji Yasunaga
  • Journal Title: The Computer Journal Volume: 印刷中 Pages: 711-728
  • DOI: 10.1093/comjnl/bxw094
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Sankaku-tori: An Old Western-Japanese Game Played on a Point Set (2017)
  • Author(s): Takashi Horiyama, Takashi Iizuka, Masashi Kiyomi, Yoshio Okamoto, Ryuhei Uehara, Takeaki Uno, Yushi Uno, and Yukiko Yamauchi
  • Journal Title: Journal of Information Processing Volume: 25 Issue: 0 Pages: 708-715
  • DOI: 10.2197/ipsjjip.25.708
  • NAID: 130005990917
  • ISSN: 1882-6652
  • Peer Reviewed
• [Journal Article] Reconfiguration of Maximum-Weight b-Matchings in a Graph (2017)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Proceedings of 23rd Annual International Computing and Combinatorics Conference (COCOON 2017) Volume: --- Pages: 287-296
  • DOI: 10.1007/978-3-319-62389-4_24
  • NAID: 120006960832
  • ISBN: 9783319623887, 9783319623894
  • Peer Reviewed / Open Access
• [Journal Article] Folding Free-Space Diagrams: Computing the Frechet Distance between 1-Dimensional Curves (Multimedia Contribution (2017)
  • Author(s): Kevin Buchin, Jinhee Chun, Maarten Loffler, Aleksandar Markovic, Wouter Meulemans, Yoshio Okamoto, and Taichi Shiitada
  • Journal Title: Proceedings of 33rd International Symposium on Computational Geometry (SoCG 2017) Volume: ---
  • DOI: 10.4230/LIPIcs.SoCG.2017.64
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Balanced line separators of unit disk graphs (2017)
  • Author(s): Paz Carmi, Man Kwun Chiu, Matthew J. Katz, Matias Korman, Yoshio Okamoto, Andre van Renssen, Marcel Roeloffzen, Taichi Shiitada, and Shakhar Smorodinsky
  • Journal Title: Proceedings of 15th Algorithms and Data Structures Symposium (WADS 2017) Volume: --- Pages: 241-252
  • DOI: 10.1007/978-3-319-62127-2_21
  • ISBN: 9783319621265, 9783319621272
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain (2017)
  • Author(s): Man-Kwun Chiu, Elena Khramtcova, Matias Korman, Aleksandar Markovic, Yoshio Okamoto, Aurelien Ooms, Andre van Renssen, Marcel Roeloffzen
  • Journal Title: arXiv preprint Volume: ---
  • Open Access / Int'l Joint Research
• [Journal Article] Computing the L1 geodesic diameter and center of a polygonal domain (2017)
  • Author(s): S. W. Bae, M. Korman, J. S. B. Mitchell, Y. Okamoto, V. Polishchuk, and H. Wang. . , pages 1-28, 2016
  • Journal Title: Discrete & Computational Geometry Volume: 57(3) Issue: 3 Pages: 674-701
  • DOI: 10.1007/s00454-016-9841-z
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Sequentially Swapping Colored Tokens on Graphs (2017)
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takashi Horiyama, Akitoshi Kawamura, Shin-Ichi Nakano, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno
  • Journal Title: Proceedings of 11th International Conference and Workshop on Algorithms and Computation (WALCOM 2017) Volume: - Pages: 435-447
  • DOI: 10.1007/978-3-319-53925-6_34
  • NAID: 120006779053
  • ISBN: 9783319539249, 9783319539256
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Approximation and Hardness of Token Swapping (2017)
  • Author(s): Tillmann Miltzow, Lothar Narins, Yoshio Okamoto, Gunter Rote, Antonis Thomas, Takeaki Uno
  • Journal Title: Proceedings of 24th European Symposium on Algorithms (ESA 2016) Volume: - Pages: 1-15
  • DOI: 10.4230/LIPIcs.ESA.2016.66
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Extended formulations for sparsity matroids (2016)
  • Author(s): Satoru Iwata, Naoyuki Kamiyama, Naoki Katoh, Shuji Kijima, and Yoshio Okamoto
  • Journal Title: Mathematical Programming Volume: 印刷中 Issue: 1-2 Pages: 565-574
  • DOI: 10.1007/s10107-015-0936-8
  • Peer Reviewed
• [Journal Article] On problems as hard as CNF-SAT (2016)
  • Author(s): Marek Cygan, Holger Dell, Daniel Lokshtanov, Daniel Marx, Jesper Nederlof, Yoshio Okamoto, Ramamohan Paturi, Saket Saurabh, Magnus Wahlstrom
  • Journal Title: ACM Transactions on Algorithms Volume: 12 Issue: 3 Pages: 1-24
  • DOI: 10.1145/2925416
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Efficient Stabilization of Cooperative Matching Games (2016)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Journal Title: Proceedings of 15th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2016) Volume: なし Pages: 41-49
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the treewidth of toroidal grids (2016)
  • Author(s): Yoshio Okamoto, Masashi Kiyomi, and Yota Otachi
  • Journal Title: Discrete Applied Mathematics Volume: 198 Pages: 303-306
  • DOI: 10.1016/j.dam.2015.06.027
  • Peer Reviewed
• [Journal Article] Computing the L1 Geodesic Diameter and Center of a Polygonal Domain (2016)
  • Author(s): Sang Won Bae, Matias Korman, Joseph Mitchell, Yoshio Okamoto, Valentin Polishchuk, and Haitao Wang
  • Journal Title: Proceedings of 33rd International Symposium on Theoretical Aspects of Computer Science (STACS 2016) Volume: ---
  • DOI: 10.4230/LIPIcs.STACS.2016.14
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Efficient Stabilization of Cooperative Matching Games (2016)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Proceedings of 15th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2016) Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Computing the Geodesic Centers of a Polygonal Domain (2016)
  • Author(s): Sang Won Bae, Matias Korman, and Yoshio Okamoto
  • Journal Title: Computational Geometry: Theory and Applications Volume: 印刷中 Pages: 3-9
  • DOI: 10.1016/j.comgeo.2015.10.009
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On problems as hard as CNF-SAT (2016)
  • Author(s): Marek Cygan, Holger Dell, Daniel Lokshtanov, Dániel Marx, Jesper Nederlof, Yoshio Okamoto, Ramamohan Paturi, Saket Saurabh, and Magnus Wahlström
  • Journal Title: ACM Transactions on Algorithms Volume: ---
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Tight Exact and Approximate Algorithmic Results on Token Swapping (2016)
  • Author(s): Tillmann Miltzow, Lothar Narins, Yoshio Okamoto, Günter Rote, Antonis Thomas, Takeaki Uno
  • Journal Title: arXiv:1602.05150 [cs.CC] Volume: ---
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Free edge lengths in plane graphs (2015)
  • Author(s): Zachary Abel, Robert Connelly, Sarah Eisenstat, Radoslav Fulek, Filip Morić, Yoshio Okamoto, Tibor Szabó, and Csaba Tóth
  • Journal Title: Discrete & Computational Geometry Volume: 54 Issue: 1 Pages: 259-289
  • DOI: 10.1007/s00454-015-9704-z
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Mind the Mind with Synchronous Clocks (2019)
  • Author(s): 岡本吉央
  • Organizer: 第14回組合せゲーム・パズル研究集会
• [Presentation] Submodular Reassignment Problem for Reallocating Agents to Tasks with Synergy Effects (2018)
  • Author(s): Yoshio Okamoto
  • Organizer: 11th Combinatorial Algorithms Day
  • Int'l Joint Research / Invited
• [Presentation] タイリングのはなし (2018)
  • Author(s): 岡本吉央
  • Organizer: 基盤(S) 離散構造処理系プロジェクト「短期滞在セミナー週間 (SSSW) 2018.07」
• [Presentation] 劣モジュラ再割当問題 (2018)
  • Author(s): 岡本吉央
  • Organizer: 本部SSOR 2018
• [Presentation] Balanced Line Separators of Unit Disk Graphs (2018)
  • Author(s): Yoshio Okamoto
  • Organizer: NWO-JSPS joint seminar: Computations on Networks with a Tree-Structure: From Theory to Practice
  • Int'l Joint Research
• [Presentation] 幾何的最短路に関わる諸問題 (2018)
  • Author(s): 岡本吉央
  • Organizer: 第30回RAMPシンポジウム
  • Invited
• [Presentation] Tight Approximability of the Server Allocation Problem for Real-Time Applications (2017)
  • Author(s): Yoshio Okamoto
  • Organizer: Combinatorial Algorithms Day
  • Int'l Joint Research / Invited
• [Presentation] 実時間アプリケーションに対するサーバ配置問題の近似(不)可能性 (2017)
  • Author(s): 伊藤 健洋，垣村 尚徳，神山 直之，小林 佑輔，岡本 吉央，後田多 太一
  • Organizer: 夏のLAシンポジウム
• [Presentation] Balanced line separators of unit disk graphs (2017)
  • Author(s): Paz Carmi, Man Kwun Chiu, Matthew J. Katz, Matias Korman, Yoshio Okamoto, Andre van Renssen, Marcel Roeloffzen, Taichi Shiitada, and Shakhar Smorodinsky
  • Organizer: 15th Algorithms and Data Structures Symposium (WADS 2017)
  • Int'l Joint Research
• [Presentation] Balanced line separators of unit disk graphs (2017)
  • Author(s): Yoshio Okamoto
  • Organizer: Shonan meeting “Geometric Graphs: Theory and Applications”
  • Int'l Joint Research / Invited
• [Presentation] ``Sphinxes in Pyramid'' and ``Sphinxes in Hexagon'' (2017)
  • Author(s): Takashi Horiyama, Ryuhei Uehara, Yoshio Okamoto
  • Organizer: 第12回組合せゲーム・パズル研究集会
  • Place of Presentation: 名古屋大学 (愛知県・名古屋市)
• [Presentation] ネットワーク型交渉ゲームの安定化アルゴリズム (2016)
  • Author(s): 伊藤 健洋，垣村 尚徳，神山 直之，小林 佑輔，岡本 吉央
  • Organizer: 第157回情報処理学会アルゴリズム研究会
  • Place of Presentation: 電気通信大学 (東京都調布市)
  • Year and Date: 2016-03-06
• [Presentation] Swapping Labeled Tokens on Graphs (2016)
  • Author(s): Yoshio Okamoto
  • Organizer: Dutch-Japanese bilateral seminar on kinetic geometric networks
  • Place of Presentation: 蔵王センタープラザ (山形県・山形市)
  • Int'l Joint Research / Invited
• [Presentation] Path-related problems in polygonal domains (2016)
  • Author(s): Yoshio Okamoto
  • Organizer: Lorentz Workshop ``Fixed-Parameter Computational Geometry''
  • Place of Presentation: ライデン (オランダ)
  • Int'l Joint Research / Invited
• [Presentation] Efficient Stabilization of Cooperative Matching Games (2016)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Organizer: 15th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2016)
  • Place of Presentation: シンガポール (シンガポール)
  • Int'l Joint Research
• [Presentation] Angular Resolution --- Around Vertices and Crossings (2016)
  • Author(s): Yoshio Okamoto
  • Organizer: Shonan Seminar ``Algorithmics for Beyond Planar Graphs''
  • Place of Presentation: 湘南国際村センター (神奈川県・葉山町)
  • Int'l Joint Research / Invited
• [Presentation] Non-Planar Graph Drawing (2015)
  • Author(s): 岡本 吉央
  • Organizer: トポロジーとコンピュータ2015
  • Place of Presentation: 日本大学文理学部 (東京都世田谷区)
  • Year and Date: 2015-11-07
  • Invited
• [Presentation] 行列の分解と組合せ最適化問題の拡張定式化 (2015)
  • Author(s): 岡本 吉央
  • Organizer: RIMS 共同研究「組合せ最適化セミナー」
  • Place of Presentation: 京都大学数理解析研究所 (京都府京都市)
  • Year and Date: 2015-07-23
  • Invited