A parallel algorithmic version of the Local Lemma

The Lov´asz Local Lemma is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of loosing a little in the estimates. His method does not seem to be parallelizable. Here we modify his technique and achieve an algorithmic version that can be parallelized, thus obtaining deterministic NC1 algorithms for several interesting algorithmic problems. ∗ Research supported in part by a United States Israel BSF Grant and by a Bergmann Memorial Grant 0 

• Type: Conference
• Year: 1991
• Where: FOCS
• Authors: Noga Alon
• Keywords: Algorithmic, Algorithmic Problems, Existence Proofs, FOCS 1991, Theoretical Computer Science