Abstract
The study of random instances of NP complete and coNP complete problems has had much impact on our understanding of the nature of hard problems as well as the strength and weakness of well-founded heuristics. This work is part of our effort to extend this line of research to intractable parameterized problems. We consider instances of the threshold dominating clique problem and the weighted satisfiability under some natural instance distribution.We study the threshold behavior of the solution probability and analyze some simple (polynomial-time) algorithms for satisfiable random instances. The behavior of these simple algorithms may help shed light on the observation that small-sized backdoor sets can be effectively exploited by some randomized DPLL-style solvers. We establish lower bounds for a parameterized version of the ordered DPLL resolution proof procedure for unsatisfiable random instances.
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