English
Related papers

Related papers: Towards Optimal Distributed Delta Coloring

200 papers

This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…

Data Structures and Algorithms · Computer Science 2020-06-23 Shay Solomon , Nicole Wein

Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper we present a new algorithm for $(\Delta+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-03-13 Yi-Jun Chang , Wenzheng Li , Seth Pettie

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 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

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

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

We present a new approach to randomized distributed graph coloring that is simpler and more efficient than previous ones. In particular, it allows us to tackle the $(\operatorname{deg}+1)$-list-coloring (D1LC) problem, where each node $v$…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-02 Magnús M. Halldórsson , Fabian Kuhn , Alexandre Nolin , Tigran Tonoyan

We show that the $(degree+1)$-list coloring problem can be solved deterministically in $O(D \cdot \log n \cdot\log^2\Delta)$ rounds in the \CONGEST model, where $D$ is the diameter of the graph, $n$ the number of nodes, and $\Delta$ the…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-04-08 Philipp Bamberger , Fabian Kuhn , Yannic Maus

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

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

Understanding the role of randomness when solving locally checkable labeling (LCL) problems in the LOCAL model has been one of the top priorities in the research on distributed graph algorithms in recent years. For LCL problems in…

Data Structures and Algorithms · Computer Science 2025-10-27 Sebastian Brandt , Fabian Kuhn , Zahra Parsaeian

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 study the edge-coloring problem in simple $n$-vertex $m$-edge graphs with maximum degree $\Delta$. This is one of the most classical and fundamental graph-algorithmic problems. Vizing's celebrated theorem provides…

Data Structures and Algorithms · Computer Science 2024-07-10 Michael Elkin , Ariel Khuzman

The celebrated palette sparsification result of [Assadi, Chen, and Khanna SODA'19] shows that to compute a $\Delta+1$ coloring of the graph, where $\Delta$ denotes the maximum degree, it suffices if each node limits its color choice to…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-04-13 Maxime Flin , Mohsen Ghaffari , Magnús M. Halldórsson , Fabian Kuhn , Alexandre Nolin

The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…

Data Structures and Algorithms · Computer Science 2025-01-08 Sebastian Brandt , Yannic Maus , Ananth Narayanan , Florian Schager , Jara Uitto

We present a simple randomized algorithm that can efficiently maintain a $(\Delta+1)$ coloring as the graph undergoes edge insertion and deletion updates, where $\Delta$ denotes an upper bound on the maximum degree. A key advantage is the…

Data Structures and Algorithms · Computer Science 2025-12-11 Mohsen Ghaffari , Jaehyun Koo

In this paper, we consider distributed coloring for planar graphs with a small number of colors. We present an optimal (up to a constant factor) $O(\log{n})$ time algorithm for 6-coloring planar graphs. Our algorithm is based on a novel…

Data Structures and Algorithms · Computer Science 2018-04-03 Shiri Chechik , Doron Mukhtar

We give a new randomized distributed algorithm for $(\Delta+1)$-coloring in the LOCAL model, running in $O(\sqrt{\log \Delta})+ 2^{O(\sqrt{\log \log n})}$ rounds in a graph of maximum degree~$\Delta$. This implies that the…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris , Johannes Schneider , Hsin-Hao Su

This paper is centered on the complexity of graph problems in the well-studied LOCAL model of distributed computing, introduced by Linial [FOCS '87]. It is widely known that for many of the classic distributed graph problems (including…

Data Structures and Algorithms · Computer Science 2017-10-31 Mohsen Ghaffari , Fabian Kuhn , Yannic Maus

We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This…

Data Structures and Algorithms · Computer Science 2020-09-15 Artur Czumaj , Peter Davies , Merav Parter