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The graph coloring problem (GCP) is a classic combinatorial optimization problem that aims to find the minimum number of colors assigned to vertices of a graph such that no two adjacent vertices receive the same color. GCP has been…

Discrete Mathematics · Computer Science 2025-06-10 Enqiang Zhu , Yu Zhang , Haopeng Sun , Ziqi Wei , Witold Pedrycz , Chanjuan Liu , Jin Xu

In the online disjoint set covers problem, the edges of a hypergraph are revealed online, and the goal is to partition them into a maximum number of disjoint set covers. That is, n nodes of a hypergraph are given at the beginning, and then…

Data Structures and Algorithms · Computer Science 2025-01-14 Marcin Bienkowski , Jarosław Byrka , Łukasz Jeż

We study the awake complexity of graph problems that belong to the class O-LOCAL, which includes a subset of problems solvable by sequential greedy algorithms, such as $(\Delta+1)$-coloring and maximal independent set. It is known from…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-11-26 Alkida Balliu , Pierre Fraigniaud , Dennis Olivetti , Mikaël Rabie

The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-20 Yi-Jun Chang , Qizheng He , Wenzheng Li , Seth Pettie , Jara Uitto

The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…

Discrete Mathematics · Computer Science 2025-02-28 Jan Bok , Jiří Fiala , Nikola Jedličková , Jan Kratochvíl , Micheala Seifrtová

We revisit asynchronous computing in networks of crash-prone processes, under the asynchronous variant of the standard LOCAL model, recently introduced by Fraigniaud et al. [DISC 2022]. We focus on the vertex coloring problem, and our…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-21 Alkida Balliu , Pierre Fraigniaud , Patrick Lambein-Monette , Dennis Olivetti , Mikael Rabie

In this paper we propose a deterministic algorithm for approximately counting the $k$-colourings of sparse random graphs $G(n,d/n)$. In particular, our algorithm computes in polynomial time a $(1\pm n^{-\Omega(1)})$approximation of the…

Discrete Mathematics · Computer Science 2020-08-12 Charilaos Efthymiou

We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…

Computational Complexity · Computer Science 2020-09-18 Hubie Chen , Bart M. P. Jansen , Karolina Okrasa , Astrid Pieterse , Paweł Rzążewski

The constructive Lov\'{a}sz Local Lemma has become a central tool for designing efficient distributed algorithms. While it has been extensively studied in the classic LOCAL model that uses unlimited bandwidth, much less is known in the…

Data Structures and Algorithms · Computer Science 2024-05-14 Magnús M. Halldórsson , Yannic Maus , Saku Peltonen

The $\hybrid$ model was recently introduced by Augustine et al. \cite{DBLP:conf/soda/AugustineHKSS20} in order to characterize from an algorithmic standpoint the capabilities of networks which combine multiple communication modes.…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-05 Ioannis Anagnostides , Themis Gouleakis

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

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

The degree splitting problem requires coloring the edges of a graph red or blue such that each node has almost the same number of edges in each color, up to a small additive discrepancy. The directed variant of the problem requires…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-12-24 Mohsen Ghaffari , Juho Hirvonen , Fabian Kuhn , Yannic Maus , Jukka Suomela , Jara Uitto

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

A distributed algorithm performs local computations on pieces of input and communicates the results through given communication links. When processing a massive graph in a distributed algorithm, local outputs must be configured as a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-12-06 Fan Chung , Olivia Simpson

This paper presents significantly improved deterministic algorithms for some of the key problems in the area of distributed graph algorithms, including network decomposition, hitting sets, and spanners. As the main ingredient in these…

Data Structures and Algorithms · Computer Science 2022-09-26 Mohsen Ghaffari , Christoph Grunau , Bernhard Haeupler , Saeed Ilchi , Václav Rozhoň

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…

A colouring of a graph G is called distinguishing if its stabiliser in Aut G is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing…

Combinatorics · Mathematics 2013-04-25 Florian Lehner

In recent years, several powerful techniques have been developed to design {\em randomized} polynomial-space parameterized algorithms. In this paper, we introduce an enhancement of color coding to design deterministic polynomial-space…

Data Structures and Algorithms · Computer Science 2017-12-20 Gregory Gutin , Felix Reidl , Magnus Wahlström , Meirav Zehavi

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…

Combinatorics · Mathematics 2021-07-08 Étienne Bamas , Louis Esperet