Distributed algorithms, the Lovász Local Lemma, and descriptive combinatorics

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...

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

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...

Sublogarithmic Distributed Algorithms for Lovász Local Lemma, and the Complexity Hierarchy

Locally Checkable Labeling (LCL) problems include essentially all the classic problems of LOCAL distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded degree graphs) that has an o(log n)-round randomized algorithm can be solved in TLLL(n) rounds, which is the randomized complexity of solving (a relaxed variant of) the Lov...