There are distributed graph algorithms for finding maximal matchings and maximal
independent sets in O (Δ+ log* n) communication rounds; here, n is the number of nodes …

Linial's famous color reduction algorithm reduces a given $ m $-coloring of a graph with
maximum degree $\Delta $ to a $ O (\Delta^ 2\log m) $-coloring, in a single round in the …

We study connections between distributed local algorithms, finitary factors of iid processes,
and descriptive combinatorics in the context of regular trees. We extend the Borel …

We prove several new tight or near-tight distributed lower bounds for classic symmetry
breaking problems in graphs. As a basic tool, we first provide a new insightful proof that any …

Given a graph G=(V,E), an (α,β)-ruling set is a subset S⊆V such that the distance between
any two vertices in S is at least α, and the distance between any vertex in V and the closest …

In this article, we present a deterministic algorithm to compute an O (k Δ)-vertex coloring in O
(Δ/k)+ log* n rounds, where Δ is the maximum degree of the network graph and k≥ 1 can be …

Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite
set of labels Σ, and for each label χ x Σ we specify what are permitted label combinations of …

Recent research revealed the existence of gaps in the complexity landscape of locally
checkable labeling (LCL) problems in the LOCAL model of distributed computing. For …

A rich line of work has been addressing the computational complexity of locally checkable
labelings (LCLs), illustrating the landscape of possible complexities. In this paper, we study …

We study the local complexity landscape of locally checkable labeling (LCL) problems on
constant-degree graphs with a focus on complexities below log* n. Our contribution is …