Design and Analysis of Algorithms for Computationally Intractable Combinatorial Problems

• Project/Area Number: 20700011
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Fundamental theory of informatics
• Research Institution: Kyoto University
• Principal Investigator: TAMAKI Suguru Kyoto University, 情報学研究科, 助教 (40432413)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 計算量理論 / アルゴリズム理論 / 厳密アルゴリズム / 充足可能性問題 / 計算困難性 / 彩色問題 / グラフ理論 / 証明の複雑さ

Research Abstract

Many practical optimization problems are known to be NP-hard, which is the class of computationally intractable problems. In this study, we gave design and complexity analysis of efficient exact algorithms for such computationally difficult problems. As a result, we obtained improved algorithms for the satisfiability problems (SAT) and the Boolean connectivity problems. We also gave characterizations of the complexity of the Boolean connectivity problems for Horn-SAT and the 3-colorability problems for planar graphs.

Research Products

• [Journal Article] On the Boolean connectivity problem for Horn relations. (2010)
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto.
  • Journal Title: Discrete Applied Mathematics 158(18) Pages: 2024-2030
• [Journal Article] The Planar Hajos Calculus for Bounded Degree Graphs. (2010)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Suguru Tamaki.
  • Journal Title: IEICE Transactions 93-A(6) Pages: 1000-1007
  • NAID: 10026864512
• [Journal Article] The complexity of the Hajos calculus for planar graphs. (2010)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Suguru Tamaki.
  • Journal Title: Theor.Comput.Sci. 411(7-9) Pages: 1182-1191
• [Journal Article] On the Boolean connectivity problem for Horn relations (2010)
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto
  • Journal Title: Discrete Applied Mathematics Volume: 158(18) Pages: 2024-2030
  • Peer Reviewed
• [Journal Article] The Planar Hajos Calculus for Bounded Degree Graphs (2010)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Suguru Tamaki
  • Journal Title: IEICE Transactions Volume: 93-A(6) Pages: 1000-1007
  • NAID: 10026864512
  • Peer Reviewed
• [Journal Article] 確率的検査可能証明と近似不可能性 (2010)
  • Author(s): 玉置卓
  • Journal Title: 電子情報通信学会 知識ベース 6群2編7章2節
• [Journal Article] The Complexity of the Hajos Calculus for Planar Graphs (2010)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Journal Title: Theoretical Computer Science 411(7-9) Pages: 1182-1191
  • Peer Reviewed
• [Journal Article] The Planar Hajos Calculus for Bounded Degree Graphs (2010)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E93-A(6)
  • NAID: 10026864512
  • Peer Reviewed
• [Journal Article] New Graph Calculi for Planar Non-3-Colorable Graphs. (2008)
  • Author(s): Youichi Hanatani, Takashi Horiyama, Kazuo Iwama, Suguru Tamaki.
  • Journal Title: IEICE Transactions 91-A(9) Pages: 2301-2307
  • NAID: 10026851334
• [Journal Article] New Graph Calculi for Planar Non-3-Colorable Graphs (2008)
  • Author(s): Y. Hanatani, T. Horiyama, K. Iwama and S. Tamaki
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A(9) Pages: 2301-2307
  • NAID: 10026851334
  • Peer Reviewed
• [Journal Article] An Exact Algorithm for the Boolean Connectivity Problem for k-CNF.Theor.
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto.
  • Journal Title: Comput.Sci. (to appear.)
• [Presentation] Improved Randomized Algorithms for 3-SAT. (2010)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Tadashi Takai, Suguru Tamaki.
  • Organizer: The 21st International Symposium on Algorithms and Computation (ISAAC)
  • Place of Presentation: Jeju Island, Korea.
  • Year and Date: 2010-12-15
• [Presentation] Improved Randomized Algorithms for 3-SAT (2010)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Tadashi Takai, Suguru Tamaki
  • Organizer: ISAAC 2010
  • Place of Presentation: Jeju Island, Korea
  • Year and Date: 2010-12-15
• [Presentation] A Query Efficient Non-adaptive Long Code Test with Perfect Completeness. (2010)
  • Author(s): Suguru Tamaki, Yuichi Yoshida.
  • Organizer: The 14th International Workshop on Randomized Techniques in Computation (APPROX-RANDOM)
  • Place of Presentation: UPC Barcelona, Spain.
  • Year and Date: 2010-09-09
• [Presentation] A Query Efficient Non-adaptive Long Code Test with Perfect Completeness (2010)
  • Author(s): Suguru Tamaki, Yuichi Yoshida
  • Organizer: APPROX-RANDOM 2010
  • Place of Presentation: UPC Barcelona, Spain
  • Year and Date: 2010-09-09
• [Presentation] An Exact Algorithm for the Boolean Connectivity Problem for k-CNF. (2010)
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto.
  • Organizer: The 13th International Conference on Theory and Applications of Satisfiability Testing (SAT)
  • Place of Presentation: Edinburgh, Scotland, UK.
  • Year and Date: 2010-07-11
• [Presentation] An Exact Algorithm for the Boolean Connectivity Problem for k-CNF (2010)
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto
  • Organizer: SAT 2010
  • Place of Presentation: Edinburgh, Scotland, UK
  • Year and Date: 2010-07-11
• [Presentation] An Exact Algorithm for the Boolean Connectivity Problem for k-CNF (2010)
  • Author(s): K.Makino, S.Tamaki, M.Yamamoto
  • Organizer: 13th International Conference on Theory and Applications of Satisfiability Testing
  • Place of Presentation: Edinburgh, Scotland
  • Year and Date: 2010-07-11
• [Presentation] Improved Randomized Algorithms for 3-SAT (2010)
  • Author(s): K.Iwama, T.Takai, S.Tamaki
  • Organizer: The 3rd AAAC Annual Meeting
  • Place of Presentation: Pohang, Korea
  • Year and Date: 2010-04-19
• [Presentation] Enumerating Non-3-colorable Planar Graphs by the Hajos Calculus (2010)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Organizer: The 3rd AAAC Annual Meeting
  • Place of Presentation: Pohang, Korea
  • Year and Date: 2010-04-17
• [Presentation] Enumerating Non-3-colorable Planar Graphs by the Hajos Calculus (2010)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Organizer: 電子情報通信学会 総合大会 DS-1-4
  • Place of Presentation: 東北大学,仙台市
  • Year and Date: 2010-03-18
• [Presentation] 3-SAT∈RTIME(0(1.3211^n)) (2010)
  • Author(s): K.Iwama, T.Takai, S.Tamaki
  • Organizer: RIMS研究集会「アルゴリズムと計算機科学の数理的基盤とその応用」
  • Place of Presentation: 京都大学,京都市
  • Year and Date: 2010-02-03
• [Presentation] Derandomizing HSSW Algorithm for 3-SAT. (2010)
  • Author(s): Kazuhisa Makino, Suguru Tamaki, Masaki Yamamoto.
  • Organizer: The 17th Annual International Computing and Combinatorics Conference (COCOON)
  • Place of Presentation: Dallas, Texas, USA.
• [Presentation] 3SATに対する乱択アルゴリズムの改良 (2010)
  • Author(s): 玉置卓
  • Organizer: ERATO湊離散構造処理系+NEO合同研究会
  • Place of Presentation: 北海道大学,札幌市(招待講演)
• [Presentation] Enumerating Non-3-colorable Planar Graphs by the Hajos Calculus. (2009)
  • Author(s): Kazuo Iwama, Kazuhisa Seto, Suguru Tamaki.
  • Organizer: 12th Korea-Japan Joint Workshop on Algorithms and Computation (WAAC)
  • Place of Presentation: Seoul, Korea.
  • Year and Date: 2009-07-04
• [Presentation] Enumerating Non-3-colorable Planar Graphs by the Hajos Calculus (2009)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Organizer: 12th Korea-Japan Joint Workshop on Algorithms and Computation
  • Place of Presentation: Seoul, Korea
  • Year and Date: 2009-07-04
• [Presentation] The Planar Hajos Calculus for Bounded Degree Graphs (2009)
  • Author(s): K.Iwama, K.Seto, S.Tamaki
  • Organizer: The 2nd AAAC Annual Meeting
  • Place of Presentation: Hangzhou, China
  • Year and Date: 2009-04-11
• [Presentation] The Planar Hajos Calculus for Bounded Degree Graphs (2009)
  • Author(s): K. Iwama, K. Seto and S. Tamaki
  • Organizer: The Second AAAC Annual Meeting
  • Place of Presentation: Hangzhou, China
  • Year and Date: 2009-04-11
• [Presentation] Hajos Calculusの計算複雑さ (2009)
  • Author(s): 玉置卓
  • Organizer: ワークショップ「離散アルゴリズムの最先端」
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-02-23
• [Presentation] An Improvement of the Soundness of a 3-Bit PCP (2009)
  • Author(s): N. Kinoshita, S. Tamaki and K. Iwama
  • Organizer: RIMS研究集会「理論計算機科学の深化と応用」
  • Place of Presentation: 京都大学
  • Year and Date: 2009-02-03
• [Presentation] The Complexity of the Hajos Calculus for Planar Graphs (2008)
  • Author(s): K. Iwama and S. Tamaki
  • Organizer: The First AAAC Annual Meeting
  • Place of Presentation: Hong Kong
  • Year and Date: 2008-04-28
• [Book] 計算量理論の最先端(離散数学のすすめ)(玉置卓)第16章 (2010)
  • Author(s): 伊藤大雄, 宇野裕之編著
  • Total Pages: 325
  • Publisher: 現代数学社
• [Book] 離散数学のすすめ (2010)
  • Author(s): 伊藤大雄, 宇野裕之編著, (玉置卓,第16章)
  • Total Pages: 325
  • Publisher: 現代数学社
• [Remarks] ホームページ等
  • URL: http://www.lab2.kuis.kyoto-u.ac.jp/~tamak/index-j.html