Sampling constraint satisfaction solutions in the local lemma regime

We give a Markov chain based algorithm for sampling almost uniform solutions of constraint satisfaction problems (CSPs). Assuming a canonical setting for the Lovász local lemma, where each constraint is violated by a small number of forbidden local configurations, our sampling algorithm is accurate in a local lemma regime, and the running time is a fixed polynomial whose dependency on n is close to linear, where n is the number of variables. Our main approach is a new technique called state compression , which generalizes the “mark/unmark” paradigm of Moitra, and can give fast local-lemma-based sampling algorithms. As concrete applications of our technique, we give the current best almost-uniform samplers for hypergraph colorings and for CNF solutions.

Authors

• Weiming Feng 0001
• Kun He 0011
• Yitong Yin

Keywords

• Lovasz Local Lemma
• Markov chain
• constraint satisfaction problem
• sampling