2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS) (2014)
Philadelphia, PA, USA
Oct. 18, 2014 to Oct. 21, 2014
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2014.59
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 Lovasz 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 algorithmic progress is measured in terms of entropy rather than energy (number of violated constraints) so that termination can be established even under the proliferation of states in which every step of the algorithm (random walk) increases the total number of violated constraints.
Image color analysis, Probabilistic logic, Educational institutions, Artificial intelligence, Computer science, Markov processes, Trajectory
D. Achlioptas and F. Iliopoulos, "Random Walks That Find Perfect Objects and the Lovasz Local Lemma," 2014 IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), Philadelphia, PA, USA, 2014, pp. 494-503.