Improved Bounds for Sampling Solutions of Random CNF Formulas

07/25/2022

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by   Kun He, et al.

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Let Φ be a random k-CNF formula on n variables and m clauses, where each clause is a disjunction of k literals chosen independently and uniformly. Our goal is, for most Φ, to (approximately) uniformly sample from its solution space. Let α=m/n be the density. The previous best algorithm runs in time n^𝗉𝗈𝗅𝗒(k,α) for any α≲2^k/300 [Galanis, Goldberg, Guo, and Yang, SIAM J. Comput.'21]. In contrast, our algorithm runs in near-linear time for any α≲2^k/3.