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A parallel algorithmic version of the Local Lemma Department of Mathematics

Summary: A parallel algorithmic version of the Local Lemma
Noga Alon
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 positive,
though very small probability. It often yields exis-
tence proofs of results without supplying any effi-
cient way of solving the corresponding algorithmic
problems. J. Beck has recently found a method for
converting some of these existence proofs into effi-
cient 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
in several points and achieve an algorithmic version
that can be parallelized, thus obtaining determinis-
tic NC1
algorithms for various interesting algorith-


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics