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Related papers: LCLs Beyond Bounded Degrees

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Understanding the role of randomness when solving locally checkable labeling (LCL) problems in the LOCAL model has been one of the top priorities in the research on distributed graph algorithms in recent years. For LCL problems in…

Data Structures and Algorithms · Computer Science 2025-10-27 Sebastian Brandt , Fabian Kuhn , Zahra Parsaeian

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

By prior work, we have many results related to distributed graph algorithms for problems that can be defined with local constraints; the formal framework used in prior work is locally checkable labeling problems (LCLs), introduced by Naor…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-07-09 Alkida Balliu , Mohsen Ghaffari , Fabian Kuhn , Augusto Modanese , Dennis Olivetti , Mikaël Rabie , Jukka Suomela , Jara Uitto

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

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

Locally Checkable Labeling (LCL) problems include essentially all the classic problems of $\mathsf{LOCAL}$ distributed algorithms. In a recent enlightening revelation, Chang and Pettie [arXiv 1704.06297] showed that any LCL (on bounded…

Data Structures and Algorithms · Computer Science 2017-05-17 Manuela Fischer , Mohsen Ghaffari

A locally checkable labeling problem (LCL) on a group $\Gamma$ asks one to find a labeling of the Cayley graph of $\Gamma$ satisfying a fixed, finite set of "local" constraints. Typical examples include proper coloring and perfect matching…

Logic · Mathematics 2026-01-28 Felix Weilacher

A Locally Checkable Labeling (LCL) is a specification describing a set of labels that are valid with respect to a set of conditions that characterize a local part of a solution to a global problem. Conditions can only refer to nodes and…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-17 Jérémie Chalopin , Maria Kokkou

In the model of \emph{local computation algorithms} (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space…

Data Structures and Algorithms · Computer Science 2015-02-16 Reut Levi , Ronitt Rubinfeld , Anak Yodpinyanee

Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-04-12 Alkida Balliu , Juho Hirvonen , Christoph Lenzen , Dennis Olivetti , Jukka Suomela

We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the…

Data Structures and Algorithms · Computer Science 2014-07-09 Bruno Courcelle , Cyril Gavoille , Mamadou Moustapha Kanté

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

By providing a new framework, we extend previous results on locally checkable problems in bounded treewidth graphs. As a consequence, we show how to solve, in polynomial time for bounded treewidth graphs, double Roman domination and Grundy…

Discrete Mathematics · Computer Science 2023-04-04 Flavia Bonomo-Braberman , Carolina Lucía Gonzalez

Shared randomness is a valuable resource in distributed computing, allowing some form of coordination between processors without explicit communication. But what happens when the shared random string can affect the inputs to the system?…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-05 Adar Hadad , Moni Naor

We investigate the connections between the fields of distributed computing and measurable combinatorics by considering complexity classes of locally checkable labeling problems on regular forests. We show that the most important…

We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-09-08 Fabian Reiter

In this paper, we introduce a new class of parameterized problems, which we call XALP: the class of all parameterized problems that can be solved in $f(k)n^{O(1)}$ time and $f(k)\log n$ space on a non-deterministic Turing Machine with…

Computational Complexity · Computer Science 2024-01-22 Hans L. Bodlaender , Carla Groenland , Hugo Jacob , Marcin Pilipczuk , Michał Pilipczuk

An impressive recent line of work has charted the complexity landscape of distributed graph algorithms. For many settings, it has been determined which time complexities exist, and which do not (in the sense that no local problem could have…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-28 Nicolas Bousquet , Laurent Feuilloley , Sébastien Zeitoun

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.…

We consider three classification systems for distributed decision tasks: With unbounded computation and certificates, defined by Balliu, D'Angelo, Fraigniaud, and Olivetti [JCSS'18], and with (two flavors of) polynomially bounded local…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-01 Laurent Feuilloley , Soumyadeep Paul , Ami Paz