解空間のパラメータ化解析による計算困難性と容易性の解明

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 15H00849
• 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: Tohoku University
• Principal Investigator: 伊藤 健洋 東北大学, 情報科学研究科, 准教授 (40431548)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2016: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
• Keywords: アルゴリズム / グラフ / 遷移問題 / 解空間の連結性 / 情報基礎

Outline of Annual Research Achievements

本年度は，シュタイナー木の遷移問題について，その計算困難性と容易性を解析した．特に，スプリットグラフでは計算困難であるが，区間グラフでは計算容易であることを示しており，グラフ構造の観点から興味深い対比を与えている．すなわち，スプリットグラフはクリークが木（スター）構造を成しているグラフであり，区間グラフはクリークがパス構造を成しているグラフである．どちらのグラフも辺が密であり，比較的近い構造を持つが，その計算複雑さに差があることを示した．
また，（リスト）辺彩色の遷移問題について，その計算困難性を示した．辺ごとに使用可能な色が限定されない辺彩色の遷移問題については，その計算困難性が一切知られていなかったが，本研究では初めて計算困難性を示すことに成功した．辺ごとに使用可能な色集合が与えられるリスト辺彩色の遷移問題は，従来研究では，彩色に使用できる色数が３色以下であれば計算容易であり，６色以上であれば計算困難であることが知られていた．すなわち，色数が４色と５色の場合は未解決であったが，本研究では，どちらも計算困難であることを証明した．これにより，色数に基づく計算困難性と容易性を完全に特徴づけることに成功した．
これら（リスト）辺彩色の遷移問題に関する計算困難性の証明は，遷移問題における帰着手法の特徴を与えることで達成している．すなわち，帰着を構成する際に，解空間の連結性を「内部連結」と「外部連結」という二つの概念を用いて保証した．これにより，複雑な帰着の正当性を計算機によって検証することを可能とした．実際，本研究で与えた証明では，可能な辺彩色が約３０万種類もあり，計算機による検証なしでは証明は難しかったであろう．

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

• [Int'l Joint Research] University of Waterloo(Canada)
• [Int'l Joint Research] Carnegie Mellon University(米国)
• [Int'l Joint Research] University of Bergen(Norway)
• [Int'l Joint Research] ウォータールー大学(カナダ)
• [Int'l Joint Research] マサチューセッツ工科大学/ブラウン大学(米国)
• [Journal Article] Approximation Algorithm for the Distance-3 Independent Set Problem on Cubic Graphs (2017)
  • Author(s): Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano
  • Journal Title: Lecture Notes in Computer Science Volume: 10167 Pages: 228-240
  • DOI: 10.1007/978-3-319-53925-6_18
  • ISBN: 9783319539249, 9783319539256
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Complexity of (List) Edge-Coloring Reconfiguration Problem (2017)
  • Author(s): Hiroki Osawa, Akira Suzuki, Takehiro Ito, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 10167 Pages: 347-358
  • DOI: 10.1007/978-3-319-53925-6_27
  • NAID: 130006300867
  • ISBN: 9783319539249, 9783319539256
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Complexity of Tiling a Polygon with Trominoes or Bars (2017)
  • Author(s): Takashi Horiyama, Takehiro Ito, Keita Nakatsuka, Akira Suzuki, Ryuhei Uehara
  • Journal Title: Discrete & Computational Geometry Volume: 印刷中 Issue: 3 Pages: 686-704
  • DOI: 10.1007/s00454-017-9884-9
  • NAID: 120006457371
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Efficient Stabilization of Cooperative Matching Games (2017)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Journal Title: Theoretical Computer Science Volume: 印刷中 Pages: 69-82
  • DOI: 10.1016/j.tcs.2017.03.020
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Complexity of Dominating Set Reconfiguration (2016)
  • Author(s): Arash Haddadan, Takehiro Ito, Amer E. Mouawad, Naomi Nishimura, Hirotaka Ono, Akira Suzuki, Youcef Tebbal
  • Journal Title: Theoretical Computer Science Volume: 651 Pages: 37-49
  • DOI: 10.1016/j.tcs.2016.08.016
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Reconfiguration of Steiner Trees in an Unweighted Graph (2016)
  • Author(s): Haruka Mizuta, Takehiro Ito, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 9843 Pages: 163-175
  • DOI: 10.1007/978-3-319-44543-4_13
  • NAID: 130007311770
  • ISBN: 9783319445427, 9783319445434
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Approximability of the Distance Independent Set Problem on Regular Graphs and Planar Graphs (2016)
  • Author(s): Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano
  • Journal Title: Lecture Notes in Computer Science Volume: 10043 Pages: 270-284
  • DOI: 10.1007/978-3-319-48749-6_20
  • ISBN: 9783319487489, 9783319487496
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Reconfiguration of Vertex Covers in a Graph (2016)
  • Author(s): Takehiro Ito, Hiroyuki Nooka, Xiao Zhou
  • Journal Title: IEICE Transactions on Information and Systems Volume: E99.D Issue: 3 Pages: 598-606
  • DOI: 10.1587/transinf.2015FCP0010
  • NAID: 130005131815
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Efficient Stabilization of Cooperative Matching Games (2016)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Journal Title: Proc. of AAMAS 2016 Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Linear-Time Algorithm for Sliding Tokens on Trees (2015)
  • Author(s): Erik D Demaine, Martin L Demaine, Eli Fox-Epstein, Duc A Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, and Takeshi Yamada
  • Journal Title: Theoretical Computer Science Volume: 600 Pages: 132-142
  • DOI: 10.1016/j.tcs.2015.07.037
  • NAID: 120006355793
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] The Complexity of Dominating Set Reconfiguration (2015)
  • Author(s): Arash Haddadan, Takehiro Ito, Amer E. Mouawad, Naomi Nishimura, Hirotaka Ono, Akira Suzuki, Youcef Tebbal
  • Journal Title: Lecture Notes in Computer Science Volume: 9214 Pages: 398-409
  • DOI: 10.1007/978-3-319-21840-3_33
  • ISBN: 9783319218397, 9783319218403
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Presentation] Approximation Algorithm for the Distance-3 Independent Set Problem on Cubic Graphs (2017)
  • Author(s): Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano
  • Organizer: The 11th International Conference and Workshops on Algorithms and Computation (WALCOM 2017)
  • Place of Presentation: Hsinchu, Taiwan
  • Year and Date: 2017-03-30
  • Int'l Joint Research
• [Presentation] The Complexity of (List) Edge-Coloring Reconfiguration Problem (2017)
  • Author(s): Hiroki Osawa, Akira Suzuki, Takehiro Ito, Xiao Zhou
  • Organizer: The 11th International Conference and Workshops on Algorithms and Computation (WALCOM 2017)
  • Place of Presentation: Hsinchu, Taiwan
  • Year and Date: 2017-03-30
  • Int'l Joint Research
• [Presentation] Approximability of the Distance Independent Set Problem on Regular Graphs and Planar Graphs (2016)
  • Author(s): Hiroshi Eto, Takehiro Ito, Zhilong Liu, Eiji Miyano
  • Organizer: The 10th Annual International Conference on Combinatorial Optimization and Applications (COCOA 2016)
  • Place of Presentation: Hong Kong, China
  • Year and Date: 2016-12-17
  • Int'l Joint Research
• [Presentation] Reconfiguration of Steiner Trees in an Unweighted Graph (2016)
  • Author(s): Haruka Mizuta, Takehiro Ito, Xiao Zhou
  • Organizer: The 27th International Workshop on Combinatorial Algorithms (IWOCA 2016)
  • Place of Presentation: Helsinki, Finland
  • Year and Date: 2016-08-17
  • Int'l Joint Research
• [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 （シンガポール共和国）
  • Year and Date: 2016-05-11
  • Int'l Joint Research
• [Presentation] The Complexity of Dominating Set Reconfiguration (2015)
  • Author(s): Arash Haddadan, Takehiro Ito, Amer E. Mouawad, Naomi Nishimura, Hirotaka Ono, Akira Suzuki, Youcef Tebbal
  • Organizer: 14th Algorithms and Data Structures Symposium (WADS 2015)
  • Place of Presentation: ビクトリア （カナダ）
  • Year and Date: 2015-08-05
  • Int'l Joint Research