  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 Lov\'{a}sz 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 sink is established by bounding
the entropy of the walk as a function of time.
