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There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…

Data Structures and Algorithms · Computer Science 2025-05-27 Manuel Jakob , Yannic Maus , Florian Schager

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

The $\Delta$-vertex coloring problem has become one of the prototypical problems for understanding the complexity of local distributed graph problems on constant-degree graphs. The major open problem is whether the problem can be solved…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-08 Manuel Jakob , Yannic Maus

Differential Privacy is the gold standard in privacy-preserving data analysis. This paper addresses the challenge of producing a differentially edge-private vertex coloring. In this paper, we present two novel algorithms to approach this…

Data Structures and Algorithms · Computer Science 2026-02-17 Michael Xie , Jiayi Wu , Dung Nguyen , Aravind Srinivasan

We investigate the distributed complexity of maximal matching and maximal independent set (MIS) in hypergraphs in the LOCAL model. A maximal matching of a hypergraph $H=(V_H,E_H)$ is a maximal disjoint set $M\subseteq E_H$ of hyperedges and…

Data Structures and Algorithms · Computer Science 2022-11-04 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti

We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings…

Data Structures and Algorithms · Computer Science 2016-08-11 Mohsen Ghaffari , Hsin-Hao Su

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

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

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

Brooks' theorem states that all connected graphs but odd cycles and cliques can be colored with $\Delta$ colors, where $\Delta$ is the maximum degree of the graph. Such colorings have been shown to admit non-trivial distributed algorithms…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-07 Yann Bourreau , Sebastian Brandt , Alexandre Nolin

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 present a local algorithm producing an independent set of expected size $0.44533n$ on large-girth 3-regular graphs and $0.40407n$ on large-girth 4-regular graphs. We also construct a cut (or bisection or bipartite subgraph) with…

Combinatorics · Mathematics 2016-02-10 Endre Csóka

We develop an experimental algorithm for the exact solving of the maximum independent set problem. The algorithm consecutively finds the maximal independent sets of vertices in an arbitrary undirected graph such that the next such set…

Data Structures and Algorithms · Computer Science 2016-03-02 Anatoly D. Plotnikov

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

By prior work, it is known that any distributed graph algorithm that finds a maximal matching requires $\Omega(\log^* n)$ communication rounds, while it is possible to find a maximal fractional matching in $O(1)$ rounds in bounded-degree…

Data Structures and Algorithms · Computer Science 2023-07-18 Sameep Dahal , Jukka Suomela

We present $O(\log\log n)$ round scalable Massively Parallel Computation algorithms for maximal independent set and maximal matching, in trees and more generally graphs of bounded arboricity, as well as for constant coloring trees.…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-11 Mohsen Ghaffari , Christoph Grunau , Ce Jin

Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem. The core innovations of the algorithm are very natural combine operations…

Data Structures and Algorithms · Computer Science 2015-02-06 Sebastian Lamm , Peter Sanders , Christian Schulz

In this paper, we present improved algorithms for the $(\Delta+1)$ (vertex) coloring problem in the Congested-Clique model of distributed computing. In this model, the input is a graph on $n$ nodes, initially each node knows only its…

Data Structures and Algorithms · Computer Science 2020-01-14 Merav Parter

One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-14 Nicolas Bousquet , Laurent Feuilloley , Marc Heinrich , Mikaël Rabie

In a fractional coloring, vertices of a graph are assigned measurable subsets of the real line and adjacent vertices receive disjoint subsets; the fractional chromatic number of a graph is at most $k$ if it has a fractional coloring in…

Combinatorics · Mathematics 2024-07-25 Tom Kelly , Luke Postle