解空間の直径に基づく計算限界解析アプローチの構築

• Project Area: A multifaceted approach toward understanding the limitations of computation
• Project/Area Number: 25106504
• 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): 2013-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2013: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: アルゴリズム / グラフ / 独立点集合 / 点彩色 / 固定パラメータ容易性

Outline of Annual Research Achievements

本年度は，点彩色を一般化した「リスト点彩色」の遷移問題に対して，詳細な解析を与えることができた．グラフ構造の指標として「パス幅」と呼ばれるパラメータがあるが，パス幅が2以上であればリスト点彩色の遷移問題はPSPACE完全であり，パス幅が1であれば多項式時間で解けることを示した．すなわち，これはリスト点彩色の遷移問題の計算困難性と容易性を，入力グラフのパス幅の観点から特徴づけたことになる．パス幅1の入力グラフに対する多項式時間アルゴリズムは動的計画法に基づいており，遷移問題に対して動的計画法を適用した例としても評価できる．

また，独立点集合の遷移問題に対しては，固定パラメータ容易性（FPT）の観点から，研究を進めることができた．この問題は，平面グラフにおいてPSPACE完全であることが示されており，解空間グラフの直径は超多項式長になる．しかし本研究では，独立点集合のサイズのみをパラメータとして，平面グラフに対するFPTアルゴリズムを与えた．この研究成果により，解空間グラフの直径が超多項式長になることを単に示すだけでなく，パラメータにどのように依存するのか解析することができた．特に，本研究では昨年度，一般のグラフに対しては，独立点集合のサイズのみをパラメータとしたFPTアルゴリズムを持ちそうにないことを証明しており，今年度の研究と対比させることで，入力グラフの構造と計算困難性の関係をより具体的に解析することができた．

この他にも，点彩色と関連が深いL(2,1)ラベリングなど，様々な遷移問題に対してアルゴリズムを開発することで，解空間グラフの直径が多項式長で抑えられる場合を明らかにし，計算困難である場合との対比を可能とした．特に，本研究では，入力グラフの構造を上手く利用することで，効率のよいアルゴリズムを多数開発することができた．

Research Progress Status

26年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

26年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Swapping Labeled Tokens on Graphs (2015)
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, Takeaki Uno
  • Journal Title: Theoretical Computer Science Volume: 印刷中 Pages: 81-94
  • DOI: 10.1016/j.tcs.2015.01.052
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs (2015)
  • Author(s): Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
  • Journal Title: IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences Volume: 印刷中
  • NAID: 130005071828
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Algorithms for the Independent Feedback Vertex Set Problem (2015)
  • Author(s): Yuma Tamura, Takehiro Ito, Xiao Zhou
  • Journal Title: IEICE Trans. on Fundamentals of Electronics, Communications and Computer Sciences Volume: 印刷中
  • NAID: 130005071827
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Reconfiguration of Cliques in a Graph (2015)
  • Author(s): Takehiro Ito, Hirotaka Ono, Yota Otachi
  • Journal Title: Lecture Notes in Computer Science Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Reconfiguration of Vertex Covers in a Graph (2015)
  • Author(s): Takehiro Ito, Hiroyuki Nooka, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 印刷中
  • NAID: 130005131815
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Deterministic Algorithms for the Independent Feedback Vertex Set Problem (2015)
  • Author(s): Yuma Tamura, Takehiro Ito, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Experimental Evaluations of Dynamic Algorithm for Maintaining Shortest-Paths Trees on Real-World Networks (2015)
  • Author(s): Takashi Hasegawa, Takehiro Ito, Akira Suzuki, Xiao Zhou
  • Journal Title: Interdisciplinary Information Sciences Volume: 21 Issue: 1 Pages: 25-35
  • DOI: 10.4036/iis.2015.25
  • NAID: 110009890454
  • ISSN: 1340-9050, 1347-6157
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Complexity of Finding Maximum Regular Induced Subgraphs with Prescribed Degree (2014)
  • Author(s): Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano
  • Journal Title: Theoretical Computer Science Volume: 550 Pages: 21-35
  • DOI: 10.1016/j.tcs.2014.07.008
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A 4.31-Approximation for the Geometric Unique Coverage Problem on Unit Disks (2014)
  • Author(s): Takehiro Ito, Shin-ichi Nakano, Yoshio Okamoto, Yota Otachi, Ryuhei Uehara, Takeaki Uno, Yushi Uno
  • Journal Title: Theoretical Computer Science Volume: 544 Pages: 14-31
  • DOI: 10.1016/j.tcs.2014.04.014
  • NAID: 120005893622
  • Peer Reviewed
• [Journal Article] Reconfigure on list L(2, 1)-labelings in a graph (2014)
  • Author(s): Takehiro Ito, Kazuto Kawamura, Hitotaka Ono and Xiao Zhou
  • Journal Title: Theoretical Computer Science (TCS) Volume: 544 Pages: 84-97
  • DOI: 10.1016/j.tcs.2014.04.011
  • NAID: 110009670153
  • Peer Reviewed
• [Journal Article] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs (2014)
  • Author(s): Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 8881 Pages: 314-328
  • DOI: 10.1007/978-3-319-12691-3_24
  • NAID: 130005071828
  • ISBN: 9783319126906, 9783319126913
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The Minimum Vulnerability Problem on Graphs (2014)
  • Author(s): Yusuke Aoki, Bjarni V. Halldorsson, Magnus M. Halldorsson, Takehiro Ito, Christian Konrad, Xiao Zhou
  • Journal Title: Lecture Notes in Computer Science Volume: 8881 Pages: 299-313
  • DOI: 10.1007/978-3-319-12691-3_23
  • ISBN: 9783319126906, 9783319126913
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Polynomial-Time Algorithm for Sliding Tokens on Trees (2014)
  • Author(s): Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada
  • Journal Title: Lecture Notes in Computer Science Volume: 8889 Pages: 389-400
  • DOI: 10.1007/978-3-319-13075-0_31
  • NAID: 120005850324
  • ISBN: 9783319130743, 9783319130750
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Fixed-Parameter Tractability of Token Jumping on Planar Graphs (2014)
  • Author(s): Takehiro Ito, Marcin Kaminski, Hirotaka Ono
  • Journal Title: Lecture Notes in Computer Science Volume: 8889 Pages: 208-219
  • DOI: 10.1007/978-3-319-13075-0_17
  • ISBN: 9783319130743, 9783319130750
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Minimum-Cost b-Edge Dominating Sets on Trees (2014)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, and Yoshio Okamoto
  • Journal Title: Lecture Notes in Computer Science Volume: 8889 Pages: 195-207
  • DOI: 10.1007/978-3-319-13075-0_16
  • ISBN: 9783319130743, 9783319130750
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Base-Object Location Problems for Base-Monotone Regions (2014)
  • Author(s): Jinhee Chun, Takashi Horiyama, Takehiro Ito, Natsuda Kaothanthong, Hirotaka Ono, Yota Otachi, Takeshi Tokuyama, Ryuhei Uehara, Takeaki Uno
  • Journal Title: Theoretical Computer Science Volume: 印刷中
  • NAID: 120005851303
  • Peer Reviewed
• [Journal Article] On the Minimum Caterpillar Problem in Digraphs (2014)
  • Author(s): Taku Okada, Akira Suzuki, Takehiro Ito and Xiao Zhou
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E97.A Issue: 3 Pages: 848-857
  • DOI: 10.1587/transfun.E97.A.848
  • NAID: 130003394790
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] Generalized rainbow connectivity of graphs (2014)
  • Author(s): Kei Uchizawa, Takanori Aoki, Takehiro Ito and Xiao Zhou
  • Journal Title: Theoretical Computer Science (TCS) Volume: 555 Pages: 35-42
  • DOI: 10.1016/j.tcs.2014.01.007
  • Peer Reviewed
• [Journal Article] On the Parameterized Complexity for Token Jumping on Graphs (2014)
  • Author(s): Takehiro Ito, Marcin Kaminski, Hirotaka Ono, Akira Suzuki, Ryuhei Uehara, Katsuhisa Yamanaka
  • Journal Title: Theory and Applications of Models of Computation, Lecture Notes in Computer Science Volume: 8402 Pages: 341-351
  • DOI: 10.1007/978-3-319-06089-7_24
  • NAID: 120005850323
  • ISBN: 9783319060880, 9783319060897
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Swapping Labeled Tokens on Graphs (2014)
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, Takeaki Uno
  • Journal Title: Lecture Notes in Computer Science Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Complexity of Finding Maximum Regular Induced Subgraphs with Prescribed Degree (2013)
  • Author(s): Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano
  • Journal Title: Proceedings of the 19th International Symposium on Fundamentals of Computation Theory (FCT2013) Volume: 8070 Pages: 28-39
  • DOI: 10.1007/978-3-642-40164-0_6
  • ISBN: 9783642401633, 9783642401640
  • Peer Reviewed
• [Presentation] Reconfiguration of Cliques in a Graph (2015)
  • Author(s): Takehiro Ito, Hirotaka Ono, Yota Otachi
  • Organizer: 12th Annual Conference on Theory and Applications of Models of Computation
  • Place of Presentation: シンガポール
  • Year and Date: 2015-05-19
• [Presentation] The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs (2014)
  • Author(s): Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou
  • Organizer: 8th Annual International Conference on Combinatorial Optimization and Applications
  • Place of Presentation: ハワイ（アメリカ）
  • Year and Date: 2014-12-20
• [Presentation] The Minimum Vulnerability Problem on Graphs (2014)
  • Author(s): Yusuke Aoki, Bjarni V. Halldorsson, Magnus M. Halldorsson, Takehiro Ito, Christian Konrad, Xiao Zhou
  • Organizer: 8th Annual International Conference on Combinatorial Optimization and Applications
  • Place of Presentation: ハワイ（アメリカ）
  • Year and Date: 2014-12-20
• [Presentation] Polynomial-Time Algorithm for Sliding Tokens on Trees (2014)
  • Author(s): Erik D. Demaine, Martin L. Demaine, Eli Fox-Epstein, Duc A. Hoang, Takehiro Ito, Hirotaka Ono, Yota Otachi, Ryuhei Uehara, Takeshi Yamada
  • Organizer: 25th Annual International Symposium on Algorithms and Computation
  • Place of Presentation: 全州（韓国）
  • Year and Date: 2014-12-16
• [Presentation] Fixed-Parameter Tractability of Token Jumping on Planar Graphs (2014)
  • Author(s): Takehiro Ito, Marcin Kaminski, Hirotaka Ono
  • Organizer: 25th Annual International Symposium on Algorithms and Computation
  • Place of Presentation: 全州（韓国）
  • Year and Date: 2014-12-15
• [Presentation] Minimum-Cost b-Edge Dominating Sets on Trees (2014)
  • Author(s): Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto
  • Organizer: 25th Annual International Symposium on Algorithms and Computation
  • Place of Presentation: 全州（韓国）
  • Year and Date: 2014-12-15
• [Presentation] Deterministic Algorithms for the Independent Feedback Vertex Set Problem (2014)
  • Author(s): Yuma Tamura, Takehiro Ito, Xiao Zhou
  • Organizer: 25th International Workshop on Combinatorial Algorithms
  • Place of Presentation: ダルース（アメリカ）
  • Year and Date: 2014-10-17
• [Presentation] Reconfiguration of Vertex Covers in a Graph (2014)
  • Author(s): Takehiro Ito, Hiroyuki Nooka, Xiao Zhou
  • Organizer: 25th International Workshop on Combinatorial Algorithms
  • Place of Presentation: ダルース（アメリカ）
  • Year and Date: 2014-10-15
• [Presentation] Complexity of Finding Maximum Regular Induced Subgraphs with Prescribed Degree
  • Author(s): Yuichi Asahiro, Hiroshi Eto, Takehiro Ito, Eiji Miyano
  • Organizer: 19th International Symposium on Fundamentals of Computation Theory
  • Place of Presentation: イギリス，リバプール
• [Presentation] On the Parameterized Complexity for Token Jumping on Graphs
  • Author(s): Takehiro Ito, Marcin Kaminski, Hirotaka Ono, Akira Suzuki, Ryuhei Uehara, Katsuhisa Yamanaka
  • Organizer: 11th Annual Conference on Theory and Applications of Models of Computation
  • Place of Presentation: インド，チェンナイ
• [Presentation] Swapping Labeled Tokens on Graphs
  • Author(s): Katsuhisa Yamanaka, Erik D. Demaine, Takehiro Ito, Jun Kawahara, Masashi Kiyomi, Yoshio Okamoto, Toshiki Saitoh, Akira Suzuki, Kei Uchizawa, Takeaki Uno
  • Organizer: 7th International Conference on FUN with Algorithms
  • Place of Presentation: イタリア，シチリア島