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Related papers: A Time Hierarchy Theorem for the LOCAL Model

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One of the cornerstones of the distributed complexity theory is the derandomization result by Chang, Kopelowitz, and Pettie [FOCS 2016]: any randomized LOCAL algorithm that solves a locally checkable labeling problem (LCL) can be…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-16 Sameep Dahal , Francesco d'Amore , Henrik Lievonen , Timothé Picavet , Jukka Suomela

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

Distributed graph coloring is one of the most extensively studied problems in distributed computing. There is a canonical family of distributed graph coloring algorithms known as the locally-iterative coloring algorithms, first formalized…

Data Structures and Algorithms · Computer Science 2023-01-31 Xinyu Fu , Yitong Yin , Chaodong Zheng

We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph.…

Neural and Evolutionary Computing · Computer Science 2021-05-27 Jakob Bossek , Frank Neumann , Pan Peng , Dirk Sudholt

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

While obtaining optimal algorithms for the most important problems in the LOCAL model has been one of the central goals in the area of distributed algorithms since its infancy, tight complexity bounds are elusive for many problems even when…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-06 Sebastian Brandt , Ananth Narayanan

In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-15 Alkida Balliu , Juho Hirvonen , Darya Melnyk , Dennis Olivetti , Joel Rybicki , Jukka Suomela

We provide novel deterministic distributed vertex coloring algorithms. As our main result, we give a deterministic distributed algorithm to compute a $(\Delta+1)$-coloring of an $n$-node graph with maximum degree $\Delta$ in…

Data Structures and Algorithms · Computer Science 2019-07-10 Fabian Kuhn

We study the problem of bi-chromatic coloring of hypergraphs in the LOCAL distributed model of computation. This problem can easily be solved by a randomized local algorithm with no communication. However, it is not known how to solve it…

Data Structures and Algorithms · Computer Science 2019-08-01 Dariusz R. Kowalski , Piotr Krysta

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

It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-15 Ken-ichi Kawarabayashi , Gregory Schwartzman

We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-06 Thomas Boudier , Fabian Kuhn , Augusto Modanese , Ronja Stimpert , Jukka Suomela

In this work we study local computation with advice: the goal is to solve a graph problem $\Pi$ with a distributed algorithm in $T(\Delta)$ communication rounds, for some function $T$ that only depends on the maximum degree $\Delta$ of the…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-25 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Krzysztof Nowicki , Dennis Olivetti , Eva Rotenberg , Jukka Suomela

Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-04-09 Ran Wolff

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…

Data Structures and Algorithms · Computer Science 2017-07-04 Susanne Albers , Sebastian Schraink

An L(2,1)-labeling of a graph $G$ is an assignment $f$ from the vertex set $V(G)$ to the set of nonnegative integers such that $|f(x)-f(y)|\ge 2$ if $x$ and $y$ are adjacent and $|f(x)-f(y)|\ge 1$ if $x$ and $y$ are at distance 2, for all…

Data Structures and Algorithms · Computer Science 2010-11-25 Toru Hasunuma , Toshimasa Ishii , Hirotaka Ono , Yushi Uno

Consider a computer network that consists of a path with $n$ nodes. The nodes are labeled with inputs from a constant-sized set, and the task is to find output labels from a constant-sized set subject to some local constraints---more…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-02-19 Alkida Balliu , Sebastian Brandt , Yi-Jun Chang , Dennis Olivetti , Mikaël Rabie , Jukka Suomela

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

Consider a graph problem that is locally checkable but not locally solvable: given a solution we can check that it is feasible by verifying all constant-radius neighborhoods, but to find a solution each node needs to explore the input graph…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-19 Will Rosenbaum , Jukka Suomela

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