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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 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 study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were…

Logic · Mathematics 2025-05-08 Katalin Berlow , Anton Bernshteyn , Clark Lyons , Felix Weilacher

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

The celebrated Time Hierarchy Theorem for Turing machines states, informally, that more problems can be solved given more time. The extent to which a time hierarchy-type theorem holds in the distributed LOCAL model has been open for many…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-04-24 Yi-Jun Chang , Seth Pettie

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

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

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

Over the past 30 years numerous algorithms have been designed for symmetry breaking problems in the LOCAL model, such as maximal matching, MIS, vertex coloring, and edge-coloring. For most problems the best randomized algorithm is at least…

Computational Complexity · Computer Science 2016-04-07 Yi-Jun Chang , Tsvi Kopelowitz , Seth Pettie

A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-03-04 Pierre Fraigniaud , Amos Korman , David Peleg

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 attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…

Data Structures and Algorithms · Computer Science 2019-06-04 Mohsen Ghaffari , Fabian Kuhn

The node-averaged complexity of a problem captures the number of rounds nodes of a graph have to spend on average to solve the problem in the LOCAL model. A challenging line of research with regards to this new complexity measure is to…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-05-03 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Gustav Schmid

A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-06 Alkida Balliu , Juho Hirvonen , Janne H. Korhonen , Tuomo Lempiäinen , Dennis Olivetti , Jukka Suomela

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

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

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

We study the local complexity landscape of locally checkable labeling (LCL) problems on constant-degree graphs with a focus on complexities below $\log^* n$. Our contribution is threefold: Our main contribution is that we complete the…

Data Structures and Algorithms · Computer Science 2022-09-26 Christoph Grunau , Vaclav Rozhon , Sebastian Brandt

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 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