Uniform Sampling Through the Lovász Local Lemma

We propose a new algorithmic framework, called partial rejection sampling , to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds new connections between the variable framework of the Lovász Local Lemma and some classical sampling algorithms such as the cycle-popping algorithm for rooted spanning trees. Among other applications, we discover new algorithms to sample satisfying assignments of k -CNF formulas with bounded variable occurrences.