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Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…

Data Structures and Algorithms · Computer Science 2021-05-17 Amin Saberi , David Wajc

In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the…

Data Structures and Algorithms · Computer Science 2022-11-15 Amirreza Akbari , Navid Eslami , Henrik Lievonen , Darya Melnyk , Joona Särkijärvi , Jukka Suomela

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

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

We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by…

Discrete Mathematics · Computer Science 2023-09-26 Mircea Marin , Temur Kutsia , Cleo Pau , Mikheil Rukhaia

Let $G$ be a graph with $n$ vertices, $m$ edges, average degree $\delta$, and maximum degree $\Delta$. The "oriented chromatic number" of $G$ is the maximum, taken over all orientations of $G$, of the minimum number of colours in a proper…

Combinatorics · Mathematics 2008-09-09 David R. Wood

Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…

Computational Complexity · Computer Science 2019-06-26 Elisabet Burjons , Fabian Frei , Edith Hemaspaandra , Dennis Komm , David Wehner

In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-29 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Joonatan Saarhelo

We give a probabilistic analysis of a Moser-type algorithm for the Lov\'{a}sz Local Lemma (LLL), adjusted to search for acyclic edge colorings of a graph. We thus improve the best known upper bound to acyclic chromatic index, also obtained…

Discrete Mathematics · Computer Science 2018-01-09 Ioannis Giotis , Lefteris Kirousis , Kostas I. Psaromiligkos , Dimitrios M. Thilikos

We study the problem of estimating the number of edges in an unknown graph. We consider a hybrid model in which an algorithm may issue independent set, degree, and neighbor queries. We show that this model admits strictly more efficient…

Data Structures and Algorithms · Computer Science 2026-01-30 Tomer Adar , Yahel Hotam , Amit Levi

A graph $G$ is \emph{locally irregular} if no two of its adjacent vertices have the same degree. In [Fioravantes et al. Complexity of finding maximum locally irregular induced subgraph. {\it SWAT}, 2022], the authors introduced and studied…

Computational Complexity · Computer Science 2025-12-17 Foivos Fioravantes , Nikolaos Melissinos , Theofilos Triommatis

Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way…

Data Structures and Algorithms · Computer Science 2017-12-11 Panagiotis Strouthopoulos , Apostolos Papadopoulos

We say that an edge colouring breaks an automorphism if some edge is mapped to an edge of a different colour. We say that the colouring is distinguishing if it breaks every non-identity automorphism. We show that such colouring can be…

Combinatorics · Mathematics 2023-06-13 Jakub Kwaśny , Marcin Stawiski

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

The maximum genus $\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal…

Combinatorics · Mathematics 2015-01-30 Michal Kotrbcik , Martin Skoviera

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for…

Combinatorics · Mathematics 2025-10-14 Péter Ágoston , Adrian Dumitrescu , Arsenii Sagdeev , Karamjeet Singh , Ji Zeng

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

We consider the problem of coloring graphs of maximum degree $\Delta$ with $\Delta$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model.…

Data Structures and Algorithms · Computer Science 2024-05-17 Yannic Maus , Magnús M. Halldórsson

We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

In the NP-hard Max $c$-Cut problem, one is given an undirected edge-weighted graph $G$ and aims to color the vertices of $G$ with $c$ colors such that the total weight of edges with distinctly colored endpoints is maximal. The case with…

Computational Complexity · Computer Science 2024-09-23 Jaroslav Garvardt , Niels Grüttemeier , Christian Komusiewicz , Nils Morawietz