Finding Planted Partitions in Random Graphs with General Degree Distributions
SIAM Journal on Discrete Mathematics
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Let I be a random 3CNF formula generated by choosing a truth assignment &phis; for variables x1, xn uniformly at random and including every clause with i literals set true by &phis; with probability pi, independently. We show that for any constants 0 ≤ η2,η3 ≤ 1 there is a constant dmin so that for all d ≥ dmin a spectral algorithm similar to the graph coloring algorithm of Alon and Kahale will find a satisfying assignment with high probability for p1 = d-n2, p2 = η2d-n2, and p3 = η3d-n2. Appropriately setting the ηi's yields natural distributions on satisfiable 3CNFs, not-all-equal-sat 3CNFs, and exactly-one-sat 3CNFs. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008