Uniform sampling through the Lovasz local lemma

ABSTRACT

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 (perhaps surprising) new connections between the variable framework of the Lovász Local Lemma and some clas- sical sampling algorithms such as the “cycle-popping” algorithm for rooted spanning trees by Wilson. Among other applications, we discover new algorithms to sample satisfying assignments of k-CNF formulas with bounded variable occurrences.

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Index Terms

• Theory of computation

  • Randomness, geometry and discrete structures

    • Generating random combinatorial structures

    • Random walks and Markov chains