Much faster algorithms for finding maximum and maximal cliques and their applications

• Project/Area Number: 25330009
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Electro-Communications
• Principal Investigator: TOMITA Etsuji 電気通信大学, その他部局等, 名誉教授 (40016598)
• Co-Investigator(Kenkyū-buntansha): 若月 光夫 電気通信大学, 大学院情報理工学研究科, 助教 (30251705) ; 西野 哲朗 電気通信大学, 大学院情報理工学研究科, 教授 (10198484) ; 伊藤 大雄 電気通信大学, 大学院情報理工学研究科, 教授 (50283487)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 最大クリーク / 極大クリーク / NP完全問題 / 時間計算量 / 分枝限定法 / 近似解法 / 多項式時間的可解性 / 疑似クリーク / 深さ優先探索 / 近似解 / 整列 / 計算機実験 / 列挙 / データマイニング

Outline of Final Research Achievements

We have developed much faster algorithms for finding a maximum clique. These have been accomplished by introducing a near-maximum clique finding algorithm and by applying appropriately sorting and coloring vertices to the underlying branch-and-bound algorithm for finding a maximum clique. The effectiveness of the above algorithms has been confirmed by extensive computational experiments. In addition, we have also given a weaker condition under that the maximum clique problem can be solved in polynomial time in theory.
Our previous algorithm for enumerating maximal cliques has been extended to have algorithms for enumerating maximal pseudo-cliques. They are confirmed to work effectively for the analysis of networks.

Research Products

• [Int'l Joint Research] The University of Pisa(Italy)
• [Journal Article] A Much Faster Algorithm for Finding a Maximum Clique with Computational Experiments (2017)
  • Author(s): TOMITA Etsuji, MATSUZAKI Sora, NAGAO Atsuki, ITO Hiro, and WAKATSUKI Mitsuo
  • Journal Title: Journal of Information Processing Volume: 25 Issue: 0 Pages: 667-677
  • DOI: 10.2197/ipsjjip.25.667
  • NAID: 130005990921
  • ISSN: 1882-6652
  • Peer Reviewed / Open Access
• [Journal Article] A Much Faster Algorithm for Finding a Maximum Clique (2016)
  • Author(s): Etsuji Tomita, Kohei Yoshida, Takuro Hatta, Atsuki Nagao, Hiro Ito and Mitsuo Wakatsuki
  • Journal Title: roceedings of the 10th International Frontiers of Algorithmics Workshop (FAW2016) Volume: 未定 Pages: 215-226
  • DOI: 10.1007/978-3-319-39817-4_21
  • ISBN: 9783319398167, 9783319398174
  • Peer Reviewed / Open Access
• [Journal Article] A Fast and Complete Algorithm for Enumerating Pseudo-Cliques in Large Graphs (2016)
  • Author(s): Hongjie Zhai, Makoto Haraguchi, Yoshiaki Okubo and Etsuji Tomita
  • Journal Title: Journal of Data Science and Analytics Volume: 2(3-4) Issue: 3-4 Pages: 145-158
  • DOI: 10.1007/s41060-016-0022-1
  • Peer Reviewed / Open Access
• [Journal Article] Enumerating Maximal Isolated Cliques Based on Vertex-Dependent Connection Lower Bound, (2016)
  • Author(s): Yoshiaki Okubo, Makoto Haraguchi and Etsuji Tomita
  • Journal Title: Proceedings of the 12th International Conference on Machine Learning and Data Mining - MLDM 2016 Volume: LNAI 9729 Pages: 569-583
  • DOI: 10.1007/978-3-319-41920-6_45
  • ISBN: 9783319419190, 9783319419206
  • Peer Reviewed
• [Journal Article] A Fast and Complete Enumeration of Pseudo-Cliques for Large Graphs (2016)
  • Author(s): Hongjie Zhai, Makoto Haraguchi, Yoshiaki Okubo and Etsuji Tomita
  • Journal Title: Proceedings of the 20th Pacific Asia Conference on Knowledge Discovery and Data Mining - PAKDD 2016 (Part I) Volume: LNAI 9651 Pages: 423-435
  • DOI: 10.1007/978-3-319-31753-3_34
  • ISBN: 9783319317526, 9783319317533
  • Peer Reviewed
• [Journal Article] Enumerating maximal clique sets with pseudo-clique constraint (2015)
  • Author(s): Hongjie Zhai, Makoto Haraguchi, Yoshiaki Okubo, Etsuji Tomita
  • Journal Title: Lecture Notes in Artificial Intelligence Volume: 9356 Pages: 324-339
  • DOI: 10.1007/978-3-319-24282-8_28
  • ISBN: 9783319242811, 9783319242828
  • Peer Reviewed
• [Journal Article] A polynomial-time algorithm for checking the equivalence of deterministic restricted one-counter transducers which accept by final state (2015)
  • Author(s): Mitsuo Wakatsuki, Etsuji Tomita, Tetsuro Nishino
  • Journal Title: Studies in Computational Intelligence, "Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing" Volume: 569 Pages: 131-144
  • DOI: 10.1007/978-3-319-10389-1_10
  • ISBN: 9783319103884, 9783319103891
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 最大クリーク問題の多項式時間的可解性の拡張の改良 (2014)
  • Author(s): 中西裕陽，富田悦次，若月光夫， 西野哲朗
  • Journal Title: 電子情報通信学会論文誌 D Volume: J97-D Pages: 1106-1121
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 最大クリーク問題の多項式時間的可解性の拡張の改良 (2014)
  • Author(s): 中西裕陽，富田悦次，若月光夫，西野哲朗
  • Journal Title: 電子情報通信学会論文誌 Volume: J97-D Pages: 1-16
  • Peer Reviewed
• [Journal Article] A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique with Computational Experiments (2013)
  • Author(s): Etsuji Tomita, Yoichi Sutani, Takanori Higashi, Mitsuo Wakatsuki
  • Journal Title: IEICE Transactions on Information and Systems Volume: E96.D Issue: 6 Pages: 1286-1298
  • DOI: 10.1587/transinf.E96.D.1286
  • NAID: 10031193989
  • ISSN: 0916-8532, 1745-1361
  • Peer Reviewed
• [Journal Article] Relational Change Pattern Mining Based on Modularity Difference (2013)
  • Author(s): Yoshiaki Okubo, Makoto Haraguchi and Etsuji Tomita
  • Journal Title: Lecture Notes in Artificial Intelligence Volume: 8271 Pages: 187-198
  • DOI: 10.1007/978-3-642-44949-9_18
  • ISBN: 9783642449482, 9783642449499
  • Peer Reviewed
• [Journal Article] A polynomial-time algorithm for checking the equivalence for real-time deterministic restricted one-counter transducers which accept by final state (2013)
  • Author(s): Mitsuo Wakatsuki, Etsuji Tomita, Tetsuro Nishino
  • Journal Title: Proc. IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing Volume: 14 Pages: 1-6
  • DOI: 10.1109/snpd.2013.18
  • Peer Reviewed
• [Presentation] 効率的な最大および極大クリーク抽出アルゴリズムとその応用 (2018)
  • Author(s): 富田悦次
  • Organizer: 電子情報通信学会中国支部学術講演会
  • Invited
• [Presentation] Efficient algorithms for finding maximum and maximal cliques and their applications (2017)
  • Author(s): Etauji Tomita
  • Organizer: The 11th International Conference and Workshops on Algorithms and Computation
  • Place of Presentation: National Chiao Tung University, Hsinchu, Taiwan
  • Year and Date: 2017-03-29
  • Int'l Joint Research / Invited
• [Presentation] Efficient algorithms for finding maximum and maximal cliques (2017)
  • Author(s): Etsuji Tomita
  • Organizer: 北海道大学大学院情報科学研究科情報理工学専攻講演会
  • Invited
• [Presentation] 最大クリーク抽出アルゴリズムMCSの高速化 (2016)
  • Author(s): 吉田幸平，八田拓郎，富田悦次，長尾篤樹，伊藤大雄，若月 光夫
  • Organizer: 情報処理学会アルゴリズム研究会
  • Place of Presentation: 電気通信大学(東京都調布市)
  • Year and Date: 2016-03-06
• [Presentation] 最終状態受理式決定性限定１カウンタ変換器の多項式時間包含性判定アルゴリズム (2016)
  • Author(s): 若月光夫, 富田悦次, 西野哲朗
  • Organizer: 冬のLAシンポジウム
  • Place of Presentation: 京都大学(京都市左京区)
  • Year and Date: 2016-01-26
• [Presentation] 可変接続数下限を用いた孤立性j-核 (2016)
  • Author(s): 趙 奇, 原口 誠, 大久保 好章, 富田悦次
  • Organizer: 人工知能学会人工知能基本問題研究会
  • Place of Presentation: 湯の原ホテル(宮城県仙台市青葉区)
  • Year and Date: 2016-01-21
• [Presentation] 大規模グラフにおける疑似クリーク厳密解全列挙に関する考察 (2015)
  • Author(s): 大久保好章，ジェイ泓杰, 原口誠, 富田悦次
  • Organizer: 情報処理学会数理モデル化と問題解決研究会
  • Place of Presentation: 電気通信大学(東京都調布市)
  • Year and Date: 2015-12-15
• [Presentation] 最大クリーク抽出アルゴリズムの高速化 (2015)
  • Author(s): 八田拓郎，富田悦次, 伊藤大雄，若月光夫
  • Organizer: 夏のLAシンポジウム
  • Place of Presentation: ゆのくに天祥(石川県加賀市)
  • Year and Date: 2015-07-14
• [Presentation] Enumerating Maximal Clique Sets with K-plex Constraint by using Meta-clique (2015)
  • Author(s): Hongjie Zhai, Makoto Haraguchi, Yoshiaki Okubo, Etsuji Tomita
  • Organizer: 人工知能学会全国大会
  • Place of Presentation: はこだて未来大学(北海道函館市)
  • Year and Date: 2015-05-30
• [Presentation] Efficient algorithms for finding maximum and maximal cliques (2015)
  • Author(s): Etsuji Tomita
  • Organizer: International Spring School on Algorithms and Applications (ISSAA 2015)
  • Place of Presentation: Bangladesh University of Engineering and Technology, Dhaka, Bangladesh
  • Year and Date: 2015-02-25
  • Invited
• [Presentation] 疑似クリーク制約を用いたクリーク族の全列挙 (2015)
  • Author(s): ジェイ泓杰, 原口誠, 大久保好章，富田悦次
  • Organizer: 人工知能学会人工知能基本問題研究会
  • Place of Presentation: 名古屋工業大学
  • Year and Date: 2015-01-13 – 2015-01-14
• [Presentation] 誘導グラフの次数下限制約に基づく疑似クリークの列挙法 (2014)
  • Author(s): ジェイ泓杰，原口 誠, 大久保好章，富田悦次
  • Organizer: 情報処理学会数理モデル化と問題解決研究会
  • Place of Presentation: 日本科学未来館
  • Year and Date: 2014-09-25 – 2014-09-26
• [Presentation] j-核性を持つ極大疑似クリークの全列挙 (2014)
  • Author(s): ジェイ泓杰,原口誠, 大久保好章，富田悦次
  • Organizer: 情報科学技術フォーラム（FIT 2014）
  • Place of Presentation: 筑波大学
  • Year and Date: 2014-09-03 – 2014-09-05
• [Presentation] 最大クリーク問題の多項式時間的可解性の拡張の更なる改良 (2014)
  • Author(s): 中西裕陽，富田悦次，若月光夫，西野哲朗
  • Organizer: 電子情報通信学会コンピュテーション研究会
  • Place of Presentation: 道後温泉 大和屋
  • Year and Date: 2014-06-13 – 2014-06-14
• [Presentation] 極大(j,k)疑似クリークの全列挙に関する一考察 (2014)
  • Author(s): 松平将宜,原口誠,大久保好章，富田悦次
  • Organizer: 人工知能学会 全国大会
  • Place of Presentation: ひめぎんホール（愛媛県県民文化会館）
  • Year and Date: 2014-05-12 – 2014-05-15
• [Presentation] 実時間決定性限定１カウンタ変換器に対する質問による多項式時間学習アルゴリズム (2014)
  • Author(s): 若月光夫，富田悦次，西野哲朗
  • Organizer: 冬のLAシンポジウム
  • Place of Presentation: 京都大学
• [Presentation] 疑似独立集合制約と正規化カットを用いたグラフの構造比較 (2013)
  • Author(s): 間澤直寛,ジェイ泓杰,原口誠,富田悦次
  • Organizer: 人工知能学会 全国大会
  • Place of Presentation: 富山国際会議場
• [Book] Journal of Discrete Algorithms (2016)
  • Author(s): Sohel Rahman, Etsuji Tomita (Eds.)
  • Total Pages: 75
  • Publisher: Elsevier
• [Book] Journal of Graph Algorithms and Applications (2016)
  • Author(s): Sohel Rahman, Etsuji Tomita (Eds.)
  • Total Pages: 158
  • Publisher: Journal of Graph Algorithms and Applications
• [Book] Clique Enumeration in "Encyclopedia of Algorithms, 2nd Edition" (2015)
  • Author(s): Etsuji Tomita
  • Total Pages: 6
  • Publisher: Springer
• [Book] Lecture Notes in Computer Science, 8973 (2015)
  • Author(s): Sohel Rahman, Etsuji Tomita (Eds.)
  • Total Pages: 336
  • Publisher: Springer
• [Book] オートマトン・言語理論 第２版 (2013)
  • Author(s): 富田悦次，横森 貴
  • Total Pages: 214
  • Publisher: 森北出版株式会社
• [Remarks] 富田研究室 ホームページ
  • URL: http://www.etlab.ice.uec.ac.jp/~tomita/index_j.html
• [Remarks] 富田研究室 ホームページ
  • URL: http://www.etlab.ice.uec.ac.jp/~tomita/index_e.html
• [Remarks] Etsuji Tomita's Home Page
  • URL: http://www.etlab.ice.uec.ac.jp/~tomita/index_e.html