We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …

The Lovász Local Lemma is a classic result in probability theory that is often used to prove
the existence of combinatorial objects via the probabilistic method. In its simplest form, it …

The probabilistic method is a technique for proving combinatorial existence results by
means of showing that a randomly chosen object has the desired properties with positive …

We present a poly $\log\log n $ time randomized CONGEST algorithm for a natural class of
Lovasz Local Lemma (LLL) instances on constant degree graphs. This implies, among other …

Asymptotic separation index is a parameter that measures how easily a Borel graph can be
approximated by its subgraphs with finite components. In contrast to the more classical …

We present ${\rm poly\log\log n} $-round randomized distributed algorithms to compute
vertex splittings, a partition of the vertices of a graph into $ k $ parts such that a node of …

The Local Computation Algorithm (LCA) model is a popular model in the field of sublinear-
time algorithms that measures the complexity of an algorithm by the number of probes the …

This text provides an introduction to the field of distributed local algorithms--an area at the
intersection of theoretical computer science and discrete mathematics. We collect many …

The constructive Lov\'{a} sz Local Lemma has become a central tool for designing efficient
distributed algorithms. While it has been extensively studied in the classic LOCAL model that …

We study complexity classes of local problems on regular trees from the perspective of
distributed local algorithms and descriptive combinatorics. We show that, surprisingly, some …