Summary: A parallel algorithmic version of the Local Lemma.
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
The Lov´asz Local Lemma is a tool that enables one to show that certain events hold with pos-
itive, 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
In a typical application of the probabilistic method we try to prove the existence of a combinatorial
structure (or a substructure of a given structure) with certain prescribed properties. To do so,