A spectral technique for random satisfiable 3CNF formulas
Abraham D. Flaxman
- pp 357-363
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It is shown 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/n 2, and p3 = η3d/ n2.Abstract:
Let I be a random 3CNF formula generated by choosing a truth assignment φ for variables x1, ..., xn uniformly at random and including every clause with i literals set true by φ with probability pi, independently. We show that for any 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 [1] will find a satisfying assignment with high probability for p1 = d/n2, p2 = η2d/n2, and p3 = η3d/n2. Appropriately setting η2 and η3 yields natural distributions on satisfiable 3CNFs, not-all-equal-sat 3CNFs, and exactly-one-sat 3CNFs.read more
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