パラメータ化計算に関する未解決問題の調査と探求による計算複雑さ解明

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 15H00853
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Osaka Prefecture University
• Principal Investigator: 宇野 裕之 大阪府立大学, 工学(系)研究科(研究院), 准教授 (60244670)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: パラメータ化計算 / アルゴリズム / 計算複雑さ / 情報基礎

Outline of Annual Research Achievements

本研究は，アルゴリズムの設計や解析，計算複雑さの理論などの分野で近年急速な進歩を見せるパラメータ化計算と，その枠組みのもとで，計算複雑さの上下界を明らかにする固定パラメータアルゴリズムやパラメータ化計算複雑さ理論を対象にしている．この際，歴史的にも未解決問題へのアプローチが分野発展の原動力となっている事実に鑑み，パラメータ化計算分野において提示される未解決問題に着目し，幅広い調査や整理とともに，過去の研究で自身が得た未解決問題との間に有機的な関連を見出し，そのような問題を解決することで，計算複雑さのクラスを分離する状況証拠を積み重ねて，困難さの原因に対する知見を獲得する．これらと並行し，さまざまな離散最適化問題に対する具体的な固定パラメータアルゴリズムや高速厳密アルゴリズムを設計することも同時に行う．これらを通じて，P=NP?問題の解決への側面からの貢献を目指す．
このような目標のもとで，本研究計画申請期間を通して，平面的有向グラフにおける最長路問題に対する劣指数時間アルゴリズム，辺グラフ枝削除問題に対する高速固定パラメータアルゴリズム，PSPACE 完全であることが知られている二人ゲーム Kayles などに対する未解決もんだいなどを幅広く調査した．それらの中で，部分問題としてグラフ描画を含む紙折り問題や，幾何学的な問題，あるいはグラフアルゴリズム分野で基礎的な問題である支配点集合問題などに対して効率的なアルゴリズムを設計することに成功した．

Research Progress Status

28年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

28年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Parameterized edge hamiltonicity (2017)
  • Author(s): Michael Lampis, Kazuhisa Makino, Valia Mitsou and Yushi Uno
  • Journal Title: Discrete Applied Mathematics Volume: 印刷中
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Subexponential fixed-parameter algorithms for partial vector domination (2016)
  • Author(s): Toshimasa Ishii, Hirotaka Ono and Yushi Uno
  • Journal Title: Discrete Optimization Volume: 22 Pages: 111-121
  • NAID: 120006533119
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] (Total) Vector domination for graphs with bounded branchwidth (2016)
  • Author(s): Toshimasa Ishii, Hirotaka Ono and Yushi Uno
  • Journal Title: Discrete Applied Mathematics Volume: 207 Pages: 80-89
  • NAID: 120006488392
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Mining preserving structures in a graph sequence (2016)
  • Author(s): Takeaki Uno and Yushi Uno
  • Journal Title: Theoretical Computer Science Volume: 654 Pages: 155-163
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Morpion Solitaire 5D: a new upper bound of 121 on the maximum score (2016)
  • Author(s): Akitoshi Kawamura, Yuichi Tatsu, Yushi Uno and Masahide Yamato
  • Journal Title: Information Processing Letters Volume: 121 Pages: 6-10
  • NAID: 110009779042
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Folding a Paper Strip to Minimize Thickness (2016)
  • Author(s): Erik D. Demaine, David Eppstein, Adam Hesterberg, Hiro Ito, Anna Lubiw, Ryuhei Uehara, Yushi Uno
  • Journal Title: Journal of Discrete Algorithms Volume: 36 Pages: 18-26
  • NAID: 120006380546
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A polynomial-time approximation scheme for the geometric unique coverage problem on unit squares (2016)
  • Author(s): Takehiro Ito, Shin-Ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno
  • Journal Title: Computational Geometry Volume: 51 Pages: 25-39
  • NAID: 120005954496
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Folding a Paper Strip to Minimize Thickness (2015)
  • Author(s): Erik D. Demaine, David Eppstein, Adam Hesterberg, Hiro Ito, Anna Lubiw, Ryuhei Uehara, Yushi Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 8973 Pages: 113-124
  • NAID: 120006380546
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Swapping Colored Tokens on Graphs (2015)
  • Author(s): Katsuhisa Yamanaka, Takashi Horiyama, David G. Kirkpatrick, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara, Yushi Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 9214 Pages: 619-628
  • NAID: 120005850327
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Mining Preserving Structures in a Graph Sequence (2015)
  • Author(s): Takeaki Uno, Yushi Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 9198 Pages: 3-15
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Hanabi is NP-complete, even for cheaters who look at their cards (2016)
  • Author(s): Jean-Francois Baffier, Man-Kwun Chiu, Yago Diez, Matias Korman, Valia Mitsou, Andre van Renssen, Marcel Roeloffzen, Yushi Uno
  • Organizer: The 8th International Conference on Fun with Algorithms
  • Place of Presentation: イタリア
  • Year and Date: 2016-06-09
  • Int'l Joint Research
• [Presentation] Threes!, Fives, 1024!, and 2048 are hard (2016)
  • Author(s): Stefan Langerman and Yushi Uno
  • Organizer: The 8th International Conference on Fun with Algorithms
  • Place of Presentation: イタリア
  • Year and Date: 2016-06-08
  • Int'l Joint Research
• [Presentation] Symmetric assembly puzzles are hard, beyond a few pieces (2015)
  • Author(s): Jason S. Ku, Erik D. Demaine, Matias Korman, Joseph Mitchell, Yota Otachi, Andre van Renssen, Marcel Roeloffzen, Ryuhei Uehara and Yushi Uno
  • Organizer: The 18th Japan Conference on Discrete and Computational Geometry and Graphs
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2015-09-15
  • Int'l Joint Research
• [Presentation] Bounds on the number of hint squares for Shakashaka (2015)
  • Author(s): Mickael Biro, Tomohisa Hamamoto, Christiane Schmidt and Yushi Uno
  • Organizer: The 18th Japan Conference on Discrete and Computational Geometry and Graphs
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2015-09-15
  • Int'l Joint Research
• [Presentation] Shortest spanning closed walks in extended theta graphs (2015)
  • Author(s): Kazuya Sakata and Yushi Uno
  • Organizer: The 18th Japan Conference on Discrete and Computational Geometry and Graphs
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2015-09-15
  • Int'l Joint Research
• [Presentation] Swapping colored tokens on graphs (2015)
  • Author(s): Katsuhisa Yamanaka, Takashi Horiyama, David Kirkpatrick, Yota Otachi, Toshiki Saitoh, Ryuhei Uehara and Yushi Uno
  • Organizer: The 13th Algorithms and Data Structures Symposium
  • Place of Presentation: Victoria, Canada
  • Year and Date: 2015-08-04
  • Int'l Joint Research
• [Presentation] Mining preserving structures in a graph sequence (2015)
  • Author(s): Takeaki Uno and Yushi Uno
  • Organizer: The 21st Annual Intermational Computing and Combinatorics Conference
  • Place of Presentation: Beijing, China
  • Year and Date: 2015-08-02
  • Int'l Joint Research
• [Book] Discrete and Computational Geometry and Graphs (2016)
  • Author(s): Jin Akiyama, Hiro Ito, Toshinori Sakai and Yushi Uno
  • Publisher: Springer