Uniform Sampling through the Lov\'asz 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 (perhaps surprising) new connections between the variable framework of the Lov\'asz 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. 
Heng Guo, Mark Jerrum, Jingcheng Liu
cs.DS math.CO math.PR