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Related papers: Near-Optimal Distributed Degree+1 Coloring

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$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…

Data Structures and Algorithms · Computer Science 2023-03-29 Mohsen Ghaffari , Christoph Grunau

We present an $O(\log^3\log n)$-round distributed algorithm for the $(\Delta+1)$-coloring problem, where each node broadcasts only one $O(\log n)$-bit message per round to its neighbors. Previously, the best such broadcast-based algorithm…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-04-20 Maxime Flin , Mohsen Ghaffari , Magnús M. Halldórsson , Fabian Kuhn , Alexandre Nolin

Distributed graph coloring is one of the most extensively studied problems in distributed computing. There is a canonical family of distributed graph coloring algorithms known as the locally-iterative coloring algorithms, first formalized…

Data Structures and Algorithms · Computer Science 2023-01-31 Xinyu Fu , Yitong Yin , Chaodong Zheng

This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e.\ with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so…

Combinatorics · Mathematics 2019-01-25 Étienne Bamas , Louis Esperet

We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings…

Data Structures and Algorithms · Computer Science 2016-08-11 Mohsen Ghaffari , Hsin-Hao Su

We present a deterministic $O(\log \log \log n)$-round low-space Massively Parallel Computation (MPC) algorithm for the classical problem of $(\Delta+1)$-coloring on $n$-vertex graphs. In this model, every machine has a sublinear local…

Data Structures and Algorithms · Computer Science 2021-12-14 Artur Czumaj , Peter Davies , Merav Parter

In this paper we present a deterministic CONGEST algorithm to compute an $O(k\Delta)$-vertex coloring in $O(\Delta/k)+\log^* n$ rounds, where $\Delta$ is the maximum degree of the network graph and $1\leq k\leq O(\Delta)$ can be freely…

Data Structures and Algorithms · Computer Science 2023-02-28 Yannic Maus

There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…

Data Structures and Algorithms · Computer Science 2025-05-27 Manuel Jakob , Yannic Maus , Florian Schager

We present a deterministic distributed algorithm in the LOCAL model that finds a proper $(\Delta + 1)$-edge-coloring of an $n$-vertex graph of maximum degree $\Delta$ in $\mathrm{poly}(\Delta, \log n)$ rounds. This is the first nontrivial…

Combinatorics · Mathematics 2021-03-08 Anton Bernshteyn

Any graph with maximum degree $\Delta$ admits a proper vertex coloring with $\Delta + 1$ colors that can be found via a simple sequential greedy algorithm in linear time and space. But can one find such a coloring via a sublinear algorithm?…

Data Structures and Algorithms · Computer Science 2019-01-08 Sepehr Assadi , Yu Chen , Sanjeev Khanna

Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-07 Yann Bourreau , Sebastian Brandt , Alexandre Nolin

Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-06-17 Maxime Flin , Magnus M. Halldorsson , Alexandre Nolin

Graph coloring is a fundamental problem in computer science. In the semi-streaming model, an input graph $G$ on $n$ vertices and maximum degree $\Delta$ is presented as a stream of edges, and the goal is to compute a vertex coloring using a…

Data Structures and Algorithms · Computer Science 2026-05-11 Shiri Chechik , Hongyi Chen , Tianyi Zhang

We present a randomized distributed algorithm that computes a $\Delta$-coloring in any non-complete graph with maximum degree $\Delta \geq 4$ in $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$ rounds, as well as a randomized algorithm that…

Data Structures and Algorithms · Computer Science 2020-08-04 Mohsen Ghaffari , Juho Hirvonen , Fabian Kuhn , Yannic Maus

We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…

Data Structures and Algorithms · Computer Science 2017-09-05 Alessandro Checco , Douglas J. Leith

The distributed (Delta + 1)-coloring problem is one of most fundamental and well-studied problems of Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms…

Distributed, Parallel, and Cluster Computing · Computer Science 2008-12-26 Leonid Barenboim , Michael Elkin

The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…

Discrete Mathematics · Computer Science 2022-04-01 Nikolaos Fryganiotis , Symeon Papavassiliou , Christos Pelekis

A recent palette sparsification theorem of Assadi, Chen, and Khanna [SODA'19] states that in every $n$-vertex graph $G$ with maximum degree $\Delta$, sampling $O(\log{n})$ colors per each vertex independently from $\Delta+1$ colors almost…

Data Structures and Algorithms · Computer Science 2020-07-03 Noga Alon , Sepehr Assadi

In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a…

Data Structures and Algorithms · Computer Science 2022-12-22 Sepehr Assadi , Amit Chakrabarti , Prantar Ghosh , Manuel Stoeckl

Graph coloring problems are among the most fundamental problems in parallel and distributed computing, and have been studied extensively in both settings. In this context, designing efficient deterministic algorithms for these problems has…

Data Structures and Algorithms · Computer Science 2024-04-26 Sam Coy , Artur Czumaj , Peter Davies , Gopinath Mishra