English
Related papers

Related papers: Is a LOCAL algorithm computable?

200 papers

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

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

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

In this work, we develop the low-space Massively Parallel Computation (MPC) complexity landscape for a family of fundamental graph problems on trees. We present a general method that solves most locally checkable labeling (LCL) problems…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-03-04 Sebastian Brandt , Rustam Latypov , Jara Uitto

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

Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…

Data Structures and Algorithms · Computer Science 2024-02-16 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Gustav Schmid

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-01 Fabian Kuhn , Thomas Moscibroda , Roger Wattenhofer

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

The question of 'what can be computed locally?' lies at the heart of distributed computing in networks. As established in Naor and Stockmeyer's seminal paper (STOC 1993), this question is undecidable, even for graph problems whose solutions…

Data Structures and Algorithms · Computer Science 2026-02-05 Lélia Blin , Fedor V. Fomin , Pierre Fraigniaud , Sylvain Gay , Petr A. Golovach , Pedro Montealegre , Ivan Rapaport , Ioan Todinca

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

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

A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-05-20 Laurent Feuilloley

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

Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…

Quantum Physics · Physics 2009-03-09 Cyril Gavoille , Adrian Kosowski , Marcin Markiewicz

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

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

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

Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…

Data Structures and Algorithms · Computer Science 2014-04-23 Omer Reingold , Shai Vardi

We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-05-01 Leonid Barenboim

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