{"type":"ScholarlyArticle","title":"Phase Transitions of Dominating Clique Problem and Their Implications to Heuristics in Satisfiability Search","authors":[{"name":"Joseph C. Culberson","slug":"joseph-c-culberson","given":"Joseph C.","family":"Culberson","affiliation":"Department of Computing Science University of Alberta Edmonton , Alberta , Canada T6G 2E8"},{"name":"Yong Gao","slug":"yong-gao","given":"Yong","family":"Gao","affiliation":"Department of Computing Science University of Alberta Edmonton , Alberta , Canada T6G 2E8"},{"name":"Calin Anton","slug":"calin-anton","given":"Calin","family":"Anton","affiliation":"Department of Computing Science University of Alberta Edmonton , Alberta , Canada T6G 2E8"}],"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 CNFtailored implementation, outperform several SAT solvers by a huge margin on dominating cliques and some other SAT problems with similar structures.","doi":null,"url":"https://ijcai.org/proceedings/2005/160","pdf":"https://ijcai.org/proceedings/2005/0160.pdf","markdown":"https://ijcai.org/proceedings/2005/160.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/160","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":160,"pages":{"first":78,"last":82},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[Franco and Gelder, 2003] J. Franco and A. V. Gelder. 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