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A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-19 Alkida Balliu , Juho Hirvonen , Dennis Olivetti , Jukka Suomela

Recently, \citeauthor*{akbari2021locality}~(ICALP 2023) studied the locality of graph problems in distributed, sequential, dynamic, and online settings from a {unified} point of view. They designed a novel $O(\log n)$-locality deterministic…

Data Structures and Algorithms · Computer Science 2024-05-02 Yi-Jun Chang , Gopinath Mishra , Hung Thuan Nguyen , Mingyang Yang , Yu-Cheng Yeh

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ region, in two settings. We present one…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-09-05 Alkida Balliu , Sebastian Brandt , Yi-Jun Chang , Dennis Olivetti , Jan Studený , Jukka Suomela

In this paper, we present the first known example of a locally checkable labeling problem (LCL) that admits asymptotic distributed quantum advantage in the LOCAL model of distributed computing: our problem can be solved in $O(\log n)$…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-08 Alkida Balliu , Filippo Casagrande , Francesco d'Amore , Massimo Equi , Barbara Keller , Henrik Lievonen , Dennis Olivetti , Gustav Schmid , Jukka Suomela

We consider the distributed complexity of the (degree+1)-list coloring problem, in which each node $u$ of degree $d(u)$ is assigned a palette of $d(u)+1$ colors, and the goal is to find a proper coloring using these color palettes. The…

Data Structures and Algorithms · Computer Science 2026-03-18 Sam Coy , Artur Czumaj , Peter Davies , Gopinath Mishra

We present a deterministic distributed algorithm, in the LOCAL model, that computes a $(1+o(1))\Delta$-edge-coloring in polylogarithmic-time, so long as the maximum degree $\Delta=\tilde{\Omega}(\log n)$. For smaller $\Delta$, we give a…

Data Structures and Algorithms · Computer Science 2017-11-16 Mohsen Ghaffari , Fabian Kuhn , Yannic Maus , Jara Uitto

We obtain better algorithms for computing more balanced orientations and degree splits in LOCAL. Important to our result is a connection to the hypergraph sinkless orientation problem [BMNSU, SODA'25] We design an algorithm of complexity…

Data Structures and Algorithms · Computer Science 2026-04-03 Yannic Maus , Alexandre Nolin , Florian Schager

$ \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 celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-24 Yi-Jun Chang , Seth Pettie

Consider an n-vertex graph G = (V,E) of maximum degree Delta, and suppose that each vertex v \in V hosts a processor. The processors are allowed to communicate only with their neighbors in G. The communication is synchronous, i.e., it…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-03-09 Leonid Barenboim , Michael Elkin

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

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

Discrete Mathematics · Computer Science 2019-06-12 George B. Mertzios , Hendrik Molter , Viktor Zamaraev

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

In this paper, we consider algorithms for edge-coloring multigraphs $G$ of bounded maximum degree, i.e., $\Delta(G) = O(1)$. Shannon's theorem states that any multigraph of maximum degree $\Delta$ can be properly edge-colored with…

Data Structures and Algorithms · Computer Science 2023-10-31 Abhishek Dhawan

We study the edge-colouring problem, and give efficient algorithms where the number of colours is parameterised by the graph's arboricity, $\alpha$. In a dynamic graph, subject to insertions and deletions, we give a deterministic algorithm…

Data Structures and Algorithms · Computer Science 2025-01-15 Aleksander B. G. Christiansen , Eva Rotenberg , Juliette Vlieghe

We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the method can transform…

Data Structures and Algorithms · Computer Science 2022-09-26 Salwa Faour , Mohsen Ghaffari , Christoph Grunau , Fabian Kuhn , Václav Rozhoň

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

We present a new technique to efficiently sample and communicate a large number of elements from a distributed sampling space. When used in the context of a recent LOCAL algorithm for $(\operatorname{degree}+1)$-list-coloring (D1LC), this…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-31 Magnús M. Halldórsson , Alexandre Nolin , Tigran Tonoyan

We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…

The Local Computation Algorithm (LCA) model is a popular model in the field of sublinear-time algorithms that measures the complexity of an algorithm by the number of probes the algorithm makes in the neighborhood of one node to determine…

Data Structures and Algorithms · Computer Science 2021-12-06 Sebastian Brandt , Christoph Grunau , Václav Rozhoň