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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

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 implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…

Computational Complexity · Computer Science 2018-02-02 Maurice Chandoo

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

The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-04-20 Yi-Jun Chang , Qizheng He , Wenzheng Li , Seth Pettie , Jara Uitto

Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…

Social and Information Networks · Computer Science 2018-10-18 Kimon Fountoulakis , David F. Gleich , Michael W. Mahoney

We study \emph{local computation algorithms (LCAs)} for constructing spanning trees. In this setting, the goal is to locally determine, for each edge $ e \in E $, whether it belongs to a spanning tree $ T $ of the input graph $ G $, where $…

Data Structures and Algorithms · Computer Science 2026-02-10 Pan Peng , Yuyang Wang

We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees. We extend the Borel determinacy technique of Marks coming from descriptive…

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

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…

Computational Complexity · Computer Science 2019-10-23 Robert Bredereck , Christian Komusiewicz , Stefan Kratsch , Hendrik Molter , Rolf Niedermeier , Manuel Sorge

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

In this paper, we show a connection between a certain online low-congestion routing problem and an online prediction of graph labeling. More specifically, we prove that if there exists a routing scheme that guarantees a congestion of…

Data Structures and Algorithms · Computer Science 2008-09-12 Jittat Fakcharoenphol , Boonserm Kijsirikul

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 drawback of the classic approach for complexity analysis of distributed graph problems is that it mostly informs about the complexity of notorious classes of ``worst case'' graphs. Algorithms that are used to prove a tight (existential)…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-06-12 Philipp Schneider

Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-08 Janne H. Korhonen , Amir Nikabadi

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…

Computational Complexity · Computer Science 2010-02-03 Bireswar Das , Samir Datta , Prajakta Nimbhorkar

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

Local clustering aims to find a compact cluster near the given starting instances. This work focuses on graph local clustering, which has broad applications beyond graphs because of the internal connectivities within various modalities.…

Social and Information Networks · Computer Science 2024-12-05 Zihao Li , Dongqi Fu , Hengyu Liu , Jingrui He

A labeled oriented graph (LOG) is an oriented graph with a labeling function from the edge set into the vertex set. The complexity of a LOG is the minimal cardinality of an initial set $S$ of vertices such that every vertex can be reached…

Combinatorics · Mathematics 2014-12-24 Moritz Christmann , Timo de Wolff

A prominent tool in many problems involving metric spaces is a notion of randomized low-diameter decomposition. Loosely speaking, $\beta$-decomposition refers to a probability distribution over partitions of the metric into sets of low…

Data Structures and Algorithms · Computer Science 2016-09-29 Lior Kamma , Robert Krauthgamer