Technical Report No. 282 - Abstract

Mohsen Ghaffari, David G. Harris, Fabian Kuhn
On Derandomizing Local Distributed Algorithms

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 randomized LOCAL algorithms and transforming them into efficient deterministic \LOCAL algorithm. We also exhibit how this simple recipe leads to significant improvements on a number of problems, in cases resolving known open problems. Two sample end-results are as follows:

- An improved distributed hypergraph maximal matching algorithm, which improves on that of Fischer, Ghaffari, and Kuhn [FOCS'17], and leads to 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 Lovász 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.