English
Related papers

Related papers: LCL problems on grids

200 papers

Locally Checkable Labeling (LCL) problems are graph problems in which a solution is correct if it satisfies some given constraints in the local neighborhood of each node. Example problems in this class include maximal matching, maximal…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-22 Alkida Balliu , Sebastian Brandt , Manuela Fischer , Rustam Latypov , Yannic Maus , Dennis Olivetti , Jara Uitto

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

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

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

The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees. A central feature of this complexity landscape is the existence of…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-17 Gustav Schmid

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

Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become…

Data Structures and Algorithms · Computer Science 2017-02-03 Pierre Fraigniaud , Marc Heinrich , Adrian Kosowski

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

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

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

We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-19 Alkida Balliu , Sebastian Brandt , Yuval Efron , Juho Hirvonen , Yannic Maus , Dennis Olivetti , 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

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

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

The Local Computation Algorithms (LCA) model is a computational model aimed at problem instances with huge inputs and output. For graph problems, the input graph is accessed using probes: strong probes (SP) specify a vertex $v$ and receive…

Data Structures and Algorithms · Computer Science 2017-03-23 Uriel Feige , Boaz Patt-Shamir , Shai Vardi

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

Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…

Information Theory · Computer Science 2015-12-21 Antti Pöllänen

In this work, we present a fast distributed algorithm for local potential problems: these are graph problems where the task is to find a locally optimal solution where no node can unilaterally improve the utility in its local neighborhood…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-20 Alkida Balliu , Thomas Boudier , Francesco d'Amore , Fabian Kuhn , Dennis Olivetti , Gustav Schmid , Jukka Suomela

A local algorithm is a distributed algorithm that completes after a constant number of synchronous communication rounds. We present local approximation algorithms for the minimum dominating set problem and the maximum matching problem in…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-02-02 Matti Åstrand , Valentin Polishchuk , Joel Rybicki , Jukka Suomela , Jara Uitto

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-12-09 Carole Delporte-Gallet , Hugues Fauconnier , Pierre Fraigniaud , Mikaël Rabie