迂回の特性を捉えた最短遷移アルゴリズムに関する研究

2023 Fiscal Year Research-status Report

• Project/Area Number: 19K11814
• Research Institution: Tohoku University
• Principal Investigator: 伊藤 健洋 東北大学, 情報科学研究科, 教授 (40431548)
• Project Period (FY): 2019-04-01 – 2025-03-31
• Keywords: 組合せ遷移 / グラフアルゴリズム

Outline of Annual Research Achievements

本年度は，Kempeら (2002年) が導入した時間ネットワークの概念において，その関連する遷移問題を研究した．この概念は，分散通信などネットワーク上の時間制約を解析するために導入され，時間ラベル付き有向グラフによって表現される．本研究では，時間制約付き有向全域木を対象とした遷移問題を解析した．これまでの研究に依って，時間制約の条件がない場合には，無向グラフであっても有向グラフであっても，任意の2つの全域木は互いに遷移可能であると知られている．すなわち，これら全域木からなる解空間グラフは常に連結である．加えて，無向・有向のいずれのグラフであっても，全域木の最短遷移問題も多項式時間で解けることが知られている．それとは対照的に，本研究では，時間制約を導入した場合には，解空間グラフは非連結となり得ることをまず示した．次に，そのような解空間グラフであっても，与えられた2つの時間制約付き有向全域木が互いに遷移可能であるかどうか（すなわち，到達判定）が，多項式時間で解けることを示した．その一方で，時間制約がある場合には最短遷移問題がNP困難であることを示し，時間制約の有無に依って計算複雑性が変わるという対比を示すことができた．
本年度は他にも，グラフ上のラベル付きトークン遷移問題に関する研究も行った．この問題では多項式長の遷移系列の存在が示せるため，最短遷移問題が研究対象となる．この問題は，量子プログラムのコンパイラ設計に現れる量子ビットルーティング問題として，これまでも研究されてきた．既存研究では実践的なアプローチが主であったが，本研究では計算複雑性の理論的な解析に取り組み，NP困難性や特殊ケースにおける多項式時間アルゴリズム等を開発した．

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

グラフに関する最短遷移問題において，これまでに本研究で開発してきたアルゴリズム手法や計算困難性の解析手法を活用して，時間制約付き有向全域木やラベル付きトークン遷移等の最短遷移問題の解析を進めることができた．また，研究成果の取りまとめも進められており，学術雑誌への論文掲載等へと繋がっている．

Strategy for Future Research Activity

コロナ禍に依る行動制限もなくなったため，海外現地での研究成果の発表を行い，参加者らからのコメントやディスカッション等を得て，本研究の成果をまとめていく予定である．その過程では，本年度のように，新たな（最短）遷移問題への開発手法の活用も試みることで，本研究に依って得られた知見や解析手法を整理していきたい．

Causes of Carryover

本研究課題は2019年度に採択されたため，その計画期間の大部分がコロナ禍の影響を受けていた．そのため，現在は行動制限がなくなったものの，本研究課題の最終的な取りまとめには，もう少し時間が必要である．次年度使用額は，研究成果の現地発表や最終的な研究成果の取りまとめを推進するために，旅費や物品購入に活用していく予定である．

Research Products

• [Int'l Joint Research] Universite de Lyon/Universite de Bordeaux/Universite Grenoble Alpes(フランス)
  • Country Name: FRANCE
  • Counterpart Institution: Universite de Lyon/Universite de Bordeaux/Universite Grenoble Alpes
• [Int'l Joint Research] University of Bremen(ドイツ)
  • Country Name: GERMANY
  • Counterpart Institution: University of Bremen
• [Journal Article] Reconfiguration of spanning trees with degree constraints or diameter constraints (2023)
  • Author(s): Nicolas Bousquet, Takehiro Ito, Yusuke Kobayashi, Haruka Mizuta, Paul Ouvrard, Akira Suzuki, Kunihiro Wasa
  • Journal Title: Algorithmica Volume: 85 Pages: 2779-2816
  • DOI: 10.1007/s00453-023-01117-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] ZDD-based algorithmic framework for solving shortest reconfiguration problems (2023)
  • Author(s): Takehiro Ito, Jun Kawahara, Yu Nakahata, Takehide Soh, Akira Suzuki, Junichi Teruyama, Takahisa Toda
  • Journal Title: Proc. of 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023), Lecture Notes in Computer Science Volume: 13884 Pages: 167-183
  • DOI: 10.1007/978-3-031-33271-5_12
  • Peer Reviewed
• [Journal Article] Fixed-parameter algorithms for graph constraint logic (2023)
  • Author(s): Tatsuhiko Hatanaka, Felix Hommelsheim, Takehiro Ito, Yusuke Kobayashi, Moritz Muhlenthaler, Akira Suzuki
  • Journal Title: Theoretical Computer Science Volume: 959 Pages: 113863
  • DOI: 10.1016/j.tcs.2023.113863
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Reconfiguration of colorings in triangulations of the sphere (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
  • Journal Title: Proc. of 39th International Symposium on Computational Geometry (SoCG 2023), Leibniz International Proceedings in Informatics Volume: 258 Pages: 43:1-43:16
  • DOI: 10.4230/LIPIcs.SoCG.2023.43
  • Peer Reviewed / Open Access
• [Journal Article] Reconfiguration of cliques in a graph (2023)
  • Author(s): Takehiro Ito, Hirotaka Ono, Yota Otachi
  • Journal Title: Discrete Applied Mathematics Volume: 333 Pages: 43-58
  • DOI: 10.1016/j.dam.2023.01.026
  • Peer Reviewed
• [Journal Article] Algorithmic theory of qubit routing (2023)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Journal Title: Proc. of 18th Algorithms and Data Structures Symposium (WADS 2023), Lecture Notes in Computer Science Volume: 14079 Pages: 533-546
  • DOI: 10.1007/978-3-031-38906-1_35
  • Peer Reviewed
• [Journal Article] Reconfiguration of time-respecting arborescences (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Naoyuki Kamiyama, Yasuaki Kobayashi, Yusuke Kobayashi, Shun-ichi Maezawa, Akira Suzuki
  • Journal Title: Proc. of 18th Algorithms and Data Structures Symposium (WADS 2023), Lecture Notes in Computer Science Volume: 14079 Pages: 521-532
  • DOI: 10.1007/978-3-031-38906-1_34
  • Peer Reviewed
• [Journal Article] Hardness of finding combinatorial shortest paths on graph associahedra (2023)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto
  • Journal Title: Proc. of 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023), Leibniz International Proceedings in Informatics Volume: 261 Pages: 82:1-82:17
  • DOI: 10.4230/LIPIcs.ICALP.2023.82
  • Peer Reviewed / Open Access
• [Journal Article] Rerouting planar curves and disjoint paths (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
  • Journal Title: Proc. of 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023), Leibniz International Proceedings in Informatics Volume: 261 Pages: 81:1-81:19
  • DOI: 10.4230/LIPIcs.ICALP.2023.81
  • Peer Reviewed / Open Access
• [Journal Article] Happy set problem on subclasses of co-comparability graphs (2023)
  • Author(s): Hiroshi Eto, Takehiro Ito, Eiji Miyano, Akira Suzuki, Yuma Tamura
  • Journal Title: Algorithmica Volume: 85 Pages: 1-21
  • DOI: 10.1007/s00453-022-01081-0
  • Peer Reviewed
• [Journal Article] Sorting balls and water: Equivalence and computational complexity (2023)
  • Author(s): Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Yota Otachi, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Katsuhisa Yamanaka, Ryo Yoshinaka
  • Journal Title: Theoretical Computer Science Volume: 978 Pages: 114158
  • DOI: 10.1016/j.tcs.2023.114158
  • Peer Reviewed
• [Journal Article] On reachable assignments under dichotomous preferences (2023)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
  • Journal Title: Theoretical Computer Science Volume: 979 Pages: 114196
  • DOI: 10.1016/j.tcs.2023.114196
  • Peer Reviewed
• [Journal Article] Solving reconfiguration problems of first-order expressible properties of graph vertices with Boolean satisfiability (2023)
  • Author(s): Takahisa Toda, Takehiro Ito, Jun Kawahara, Takehide Soh, Akira Suzuki, Junichi Teruyama
  • Journal Title: Proc. of 35th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2023) Volume: - Pages: 294-302
  • DOI: 10.1109/ICTAI59109.2023.00050
  • Peer Reviewed
• [Presentation] ZDD-based algorithmic framework for solving shortest reconfiguration problems (2023)
  • Author(s): Takehiro Ito, Jun Kawahara, Yu Nakahata, Takehide Soh, Akira Suzuki, Junichi Teruyama, Takahisa Toda
  • Organizer: 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)
  • Int'l Joint Research
• [Presentation] Reconfiguration of colorings in triangulations of the sphere (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
  • Organizer: 39th International Symposium on Computational Geometry (SoCG 2023)
  • Int'l Joint Research
• [Presentation] Hardness of finding combinatorial shortest paths on graph associahedra (2023)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto
  • Organizer: 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023)
  • Int'l Joint Research
• [Presentation] Rerouting planar curves and disjoint paths (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Yusuke Kobayashi, Shun-ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
  • Organizer: 50th EATCS International Colloquium on Automata, Languages and Programming (ICALP 2023)
  • Int'l Joint Research
• [Presentation] Reconfiguration of time-respecting arborescences (2023)
  • Author(s): Takehiro Ito, Yuni Iwamasa, Naoyuki Kamiyama, Yasuaki Kobayashi, Yusuke Kobayashi, Shun-ichi Maezawa, Akira Suzuki
  • Organizer: 18th Algorithms and Data Structures Symposium (WADS 2023)
  • Int'l Joint Research
• [Presentation] Algorithmic theory of qubit routing (2023)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Organizer: 18th Algorithms and Data Structures Symposium (WADS 2023)
  • Int'l Joint Research
• [Presentation] Solving reconfiguration problems of first-order expressible properties of graph vertices with Boolean satisfiability (2023)
  • Author(s): Takahisa Toda, Takehiro Ito, Jun Kawahara, Takehide Soh, Akira Suzuki, Junichi Teruyama
  • Organizer: 35th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2023)
  • Int'l Joint Research