Reproduce “Single-Variable Connectivity in Random $k$-SAT” on OpenResearch
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About this paper
Chunyang Wang, Yitong Yin, Yixiao Yu, Yiyao Zhang
The authors give a randomized polynomial-time algorithm that joins two supplied independent uniform satisfying assignments of random k-SAT by a satisfying path of O_k(n) single-variable flips. For sufficiently large fixed k and then n, the guarantee holds below the reconstruction threshold, at c ≤ 0.871 − 1/(ln ln k)^(1/16), with formula and algorithm success probabilities at least 1−1/n. It does not establish global connectivity.
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