Phase transitions of dominating clique problem and their implications to heuristics in satisfiability search

Authors:
Joseph Culberson;Yong Gao;Calin Anton
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada
Venue:
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Year:
2005

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Abstract

We study a monotone NP decision problem, the dominating clique problem, whose phase transition occurs at a very dense stage of the random graph evolution process. We establish the exact threshold of the phase transition and propose an efficient search algorithm that runs in super-polynomial time with high probability. Our empirical studies reveal two even more intriguing phenomena in its typical-case complexity: (1) the problem is "uniformly hard" with a tiny runtime variance on negative instances. (2) Our algorithm and its CNF-tailored implementation, outperform several SAT solvers by a huge margin on dominating cliques and some other SAT problems with similar structures.