Deterministic algorithms for the Lovász local lemma: Simpler, more general, and more parallel

Deterministic Algorithms for the Lovász Local Lemma

The Lovász Local Lemma [5] (LLL) is a powerful result in probability theory that states that the probability that none of a set of bad events happens is nonzero if the probability of each event is small compared to the number of events that depend on it. It is often used in combination with the probabilistic method for non-constructive existence proofs. A prominent application is to k-CNF formu...

Deterministic parallel algorithms for fooling polylogarithmic juntas and the Lovász Local Lemma

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with work by Luby (1988) and continuing with Berger & Rompel (1991) and Chari et al. (1994), showed that these techniques can be combined to give deterministic parallel algorithms for combinatorial opt...

Parallel algorithms for the Lopsided Lovász Local Lemma

The Lovász Local Lemma (LLL) is a probabilistic tool which shows that, if a collection of “bad” events B in a probability space are not too likely and not too interdependent, then there is a positive probability that no bad-events in B occur. Moser & Tardos (2010) gave sequential and parallel algorithms which transformed most applications of the variable-assignment LLL into efficient algorithms...

Dissertation ALGORITHMS AND GENERALIZATIONS FOR THE LOVÁSZ LOCAL LEMMA

Title of Dissertation ALGORITHMS AND GENERALIZATIONS FOR THE LOVÁSZ LOCAL LEMMA David G. Harris, Doctor of Philosophy, 2015 Dissertation directed by: Professor Aravind Srinivasan, Department of

Lovász Local Lemma