A Fast Distributed Algorithm for (Δ+ 1)-Edge-Coloring

06/28/2020
by   Anton Bernshteyn, et al.
0

We present a deterministic distributed algorithm in the LOCAL model that finds a proper (Δ + 1)-edge-coloring of an n-vertex graph of maximum degree Δ in poly(Δ, log n) rounds. This is the first nontrivial distributed edge-coloring algorithm that uses only Δ+1 colors (matching the bound given by Vizing's theorem). Our approach is inspired by the recent proof of the measurable version of Vizing's theorem due to Grebík and Pikhurko.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/02/2019

Towards the Locality of Vizing's Theorem

Vizing showed that it suffices to color the edges of a simple graph usin...
11/15/2017

Deterministic Distributed Edge-Coloring with Fewer Colors

We present a deterministic distributed algorithm, in the LOCAL model, th...
06/07/2021

A Matrix Trickle-Down Theorem on Simplicial Complexes and Applications to Sampling Colorings

We show that the natural Glauber dynamics mixes rapidly and generates a ...
02/08/2021

Superfast Coloring in CONGEST via Efficient Color Sampling

We present a procedure for efficiently sampling colors in the model. It...
09/21/2018

Distributed coloring of graphs with an optimal number of colors

This paper studies sufficient conditions to obtain efficient distributed...
05/14/2021

The Greedy Algorithm is not Optimal for On-Line Edge Coloring

Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no onlin...
07/13/2019

Cover and variable degeneracy

Let f be a nonnegative integer valued function on the vertex-set of a gr...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.