Random Walks That Find Perfect Objects and the Lovasz Local Lemma

@article{Achlioptas2014RandomWT,
  title={Random Walks That Find Perfect Objects and the Lovasz Local Lemma},
  author={Dimitris Achlioptas and Fotis Iliopoulos},
  journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
  year={2014},
  pages={494-503}
}
We give an algorithmic local lemma by establishing a sufficient condition for the uniform random walk on a directed graph to reach a sink quickly. Our work is inspired by Moser’s entropic method proof of the Lovász Local Lemma (LLL) for satisfiability and completely bypasses the Probabilistic Method formulation of the LLL. In particular, our method works when the underlying state space is entirely unstructured. Similarly to Moser’s argument, the key point is that the inevitability of reaching a… CONTINUE READING
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