On Derandomizing Local Distributed Algorithms

TL;DR

This paper presents a generic derandomization technique for local distributed algorithms, leading to improved algorithms for hypergraph matching, edge-coloring, and problems related to the Lovász Local Lemma.

Contribution

The authors introduce a simple, generic derandomization method that enhances several existing distributed algorithms and resolves open problems in the field.

Findings

Improved distributed hypergraph maximal matching algorithm.

Enhanced algorithms for edge-coloring and maximum matching approximation.

Closer to resolving the Lovász Local Lemma conjecture in distributed settings.

Abstract

The gap between the known randomized and deterministic local distributed algorithms underlies arguably the most fundamental and central open question in distributed graph algorithms. In this paper, we develop a generic and clean recipe for derandomizing LOCAL algorithms. We also exhibit how this simple recipe leads to significant improvements on a number of problem. Two main results are: - An improved distributed hypergraph maximal matching algorithm, improving on Fischer, Ghaffari, and Kuhn [FOCS'17], and giving improved algorithms for edge-coloring, maximum matching approximation, and low out-degree edge orientation. The first gives an improved algorithm for Open Problem 11.4 of the book of Barenboim and Elkin, and the last gives the first positive resolution of their Open Problem 11.10. - An improved distributed algorithm for the Lov\'{a}sz Local Lemma, which gets closer to a conjecture of Chang and Pettie [FOCS'17], and moreover leads to improved distributed algorithms for problems such as defective coloring and $k$-SAT.