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

2017 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

計算機科学