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We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a $(2\Delta-1)$-edge coloring can be…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-06-03 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti

In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…

Data Structures and Algorithms · Computer Science 2025-05-12 Yi-Jun Chang , Gopinath Mishra , Hung Thuan Nguyen , Farrel D Salim

In this paper we study fractional coloring from the angle of distributed computing. Fractional coloring is the linear relaxation of the classical notion of coloring, and has many applications, in particular in scheduling. It was proved by…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-03-15 Nicolas Bousquet , Louis Esperet , François Pirot

Given a graph $G$ with $n$ vertices and maximum degree $\Delta$, it is known that $G$ admits a vertex coloring with $\Delta + 1$ colors such that no edge of $G$ is monochromatic. This can be seen constructively by a simple greedy algorithm,…

Data Structures and Algorithms · Computer Science 2021-02-16 Jackson Morris , Fang Song

We consider coloring problems in the distributed message-passing setting. The previously-known deterministic algorithms for edge-coloring employed at least (2Delta - 1) colors, even though any graph admits an edge-coloring with Delta + 1…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-10-24 Leonid Barenboim , Michael Elkin , Tzalik Maimon

We consider graph coloring and related problems in the distributed message-passing model. {Locally-iterative algorithms} are especially important in this setting. These are algorithms in which each vertex decides about its next color only…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-20 Leonid Barenboim , Michael Elkin , Uri Goldenberg

$ \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

The problem of coloring the edges of an $n$-node graph of maximum degree $\Delta$ with $2\Delta - 1$ colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-26 Alkida Balliu , Fabian Kuhn , Dennis Olivetti

We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the $G(n,p)$ random graph model, with number of nodes $n$ and…

Data Structures and Algorithms · Computer Science 2018-04-25 Soumyottam Chatterjee , Reza Fathi , Gopal Pandurangan , Nguyen Dinh Pham

In distributed network computing, a variant of the LOCAL model has been recently introduced, referred to as the SLEEPING model. In this model, nodes have the ability to decide on which round they are awake, and on which round they are…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-17 Fabien Dufoulon , Pierre Fraigniaud , Mikaël Rabie , Hening Zheng

Coloring unit-disk graphs efficiently is an important problem in the global and distributed setting, with applications in radio channel assignment problems when the communication relies on omni-directional antennas of the same power. In…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-01-23 Louis Esperet , Sébastien Julliot , Arnaud de Mesmay

We present three sublinear randomized algorithms for vertex-coloring of graphs with maximum degree $\Delta$. The first is a simple algorithm that extends the idea of Morris and Song to color graphs with maximum degree $\Delta$ using…

Data Structures and Algorithms · Computer Science 2025-02-11 Asaf Ferber , Liam Hardiman , Xiaonan Chen

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

Recent improvements on the deterministic complexities of fundamental graph problems in the LOCAL model of distributed computing have yielded state-of-the-art upper bounds of $\tilde{O}(\log^{5/3} n)$ rounds for maximal independent set (MIS)…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-21 Yann Bourreau , Sebastian Brandt , Alexandre Nolin

We study the {edge-coloring} problem in the message-passing model of distributed computing. This is one of the most fundamental and well-studied problems in this area. Currently, the best-known deterministic algorithms for (2Delta…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-03-17 Leonid Barenboim , Michael Elkin

Let $\epsilon \in (0, 1)$ and $n, \Delta \in \mathbb N$ be such that $\Delta = \Omega\left(\max\left\{\frac{\log n}{\epsilon},\, \left(\frac{1}{\epsilon}\log \frac{1}{\epsilon}\right)^2\right\}\right)$. Given an $n$-vertex $m$-edge simple…

Data Structures and Algorithms · Computer Science 2025-02-14 Abhishek Dhawan

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

We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-06-03 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…

Data Structures and Algorithms · Computer Science 2017-11-15 Sayan Bhattacharya , Deeparnab Chakrabarty , Monika Henzinger , Danupon Nanongkai

Distributed graph algorithms that separately optimize for either the number of rounds used or the total number of messages sent have been studied extensively. However, algorithms simultaneously efficient with respect to both measures have…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-18 Bernhard Haeupler , D. Ellis Hershkowitz , David Wajc