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Related papers: Distributed $\Delta$-Coloring Plays Hide-and-Seek

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Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for…

Data Structures and Algorithms · Computer Science 2019-04-11 Hsin-Hao Su , Hoa T. Vu

We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-03 Alkida Balliu , Thomas Boudier , Sebastian Brandt , Dennis Olivetti

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

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-20 Alkida Balliu , Thomas Boudier , Francesco d'Amore , Fabian Kuhn , Dennis Olivetti , Gustav Schmid , Jukka Suomela

As the main contribution of this work we present deterministic edge coloring algorithms in the CONGEST model. In particular, we present an algorithm that edge colors any $n$-node graph with maximum degree $\Delta$ with with…

Data Structures and Algorithms · Computer Science 2026-03-04 Joakim Blikstad , Yannic Maus , Tijn de Vos

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

Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…

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

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

There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-13 Alkida Balliu , Sebastian Brandt , Juho Hirvonen , Dennis Olivetti , Mikaël Rabie , Jukka Suomela

Graph coloring is one of the central problems in distributed graph algorithms. Much of the research on this topic has focused on coloring with $\Delta+1$ colors, where $\Delta$ denotes the maximum degree. Using $\Delta+1$ colors may be…

Data Structures and Algorithms · Computer Science 2017-08-24 Mohsen Ghaffari , Christiana Lymouri

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

Very recently, Khoury and Schild [FOCS 2025] showed that any randomized LOCAL algorithm that solves maximal matching requires $\Omega(\min\{\log \Delta, \log_\Delta n\})$ rounds, where $n$ is the number of nodes in the graph and $\Delta$ is…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-21 Alkida Balliu , Filippo Casagrande , Francesco d'Amore , Dennis Olivetti

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

The distributed coloring problem is arguably one of the key problems studied in the area of distributed graph algorithms. The most standard variant of the problem asks for a proper vertex coloring of a graph with $\Delta+1$ colors, where…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-05 Marc Fuchs , Fabian Kuhn

Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…

Data Structures and Algorithms · Computer Science 2021-04-13 Magnús M. Halldórsson , Fabian Kuhn , Yannic Maus , Tigran Tonoyan

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…

Data Structures and Algorithms · Computer Science 2017-07-04 Susanne Albers , Sebastian Schraink

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

We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel determinacy technique of Marks coming from descriptive…

Recent work on distributed graph algorithms [e.g. STOC 2022, ITCS 2022, PODC 2020] has drawn attention to the following open question: are round elimination fixed points a universal technique for proving lower bounds? That is, given a…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-27 Alkida Balliu , Sebastian Brandt , Ole Gabsdil , Dennis Olivetti , Jukka Suomela

We give a new randomized distributed algorithm for the $\Delta+1$-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-12 Magnús M. Halldórsson , Alexandre Nolin , Tigran Tonoyan