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Related papers: A Lower Bound for the Distributed Lov\'asz Local L…

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There are distributed graph algorithms for finding maximal matchings and maximal independent sets in $O(\Delta + \log^* n)$ communication rounds; here $n$ is the number of nodes and $\Delta$ is the maximum degree. The lower bound by Linial…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-13 Alkida Balliu , Sebastian Brandt , Juho Hirvonen , 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

The Lov\'asz Local Lemma is a classic result in probability theory that is often used to prove the existence of combinatorial objects via the probabilistic method. In its simplest form, it states that if we have $n$ `bad events', each of…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-10-20 Peter Davies

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

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

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 Lov\'asz Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of $n$ `bad events', each occurring with probability at most $p$ and dependent on a set of underlying random variables,…

Data Structures and Algorithms · Computer Science 2025-02-18 Peter Davies-Peck

We consider the problem of coloring graphs of maximum degree $\Delta$ with $\Delta$ colors in the distributed setting with limited bandwidth. Specifically, we give a $\mathsf{poly}\log\log n$-round randomized algorithm in the CONGEST model.…

Data Structures and Algorithms · Computer Science 2024-05-17 Yannic Maus , Magnús M. Halldórsson

In this work, we study the Lov\'asz local lemma (LLL) problem in the area of distributed quantum computing, which has been the focus of attention of recent advances in quantum computing [STOC'24, STOC'25, STOC'25]. We prove a lower bound of…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-20 Sebastian Brandt , Tim Göttlicher

We present a poly $\log \log n$ time randomized CONGEST algorithm for a natural class of Lovasz Local Lemma (LLL) instances on constant degree graphs. This implies, among other things, that there are no LCL problems with randomized…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-08-06 Yannic Maus , Jara Uitto

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…

Data Structures and Algorithms · Computer Science 2020-06-09 Sebastian Brandt , Christoph Grunau , Václav Rozhoň

We study lower bounds on information dissemination in adversarial dynamic networks. Initially, k pieces of information (henceforth called tokens) are distributed among n nodes. The tokens need to be broadcast to all nodes through a…

Data Structures and Algorithms · Computer Science 2012-08-31 Bernhard Haeupler , Fabian Kuhn

Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-06-03 Alkida Balliu , Sebastian Brandt , Dennis Olivetti

We present ${\rm poly\log\log n}$-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into $k$ parts such that a node of degree $d(u)$ has $\approx d(u)/k$ neighbors in each part. Our…

Data Structures and Algorithms · Computer Science 2022-08-18 Magnús M. Halldórsson , Yannic Maus , Alexandre Nolin

The last five years of research on distributed graph algorithms have seen huge leaps of progress, both regarding algorithmic improvements and impossibility results: new strong lower bounds have emerged for many central problems and…

Data Structures and Algorithms · Computer Science 2025-01-08 Sebastian Brandt , Yannic Maus , Ananth Narayanan , Florian Schager , Jara Uitto

We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…

Data Structures and Algorithms · Computer Science 2024-04-05 Lukas Michel , Alex Scott

This paper concerns {\em randomized} leader election in synchronous distributed networks. A distributed leader election algorithm is presented for complete $n$-node networks that runs in O(1) rounds and (with high probability) uses only…

Data Structures and Algorithms · Computer Science 2013-05-16 Shay Kutten , Gopal Pandurangan , David Peleg , Peter Robinson , Amitabh Trehan

By prior work, it is known that any distributed graph algorithm that finds a maximal matching requires $\Omega(\log^* n)$ communication rounds, while it is possible to find a maximal fractional matching in $O(1)$ rounds in bounded-degree…

Data Structures and Algorithms · Computer Science 2023-07-18 Sameep Dahal , Jukka Suomela

We give a randomized $\Delta$-coloring algorithm in the LOCAL model that runs in $\text{poly} \log \log n$ rounds, where $n$ is the number of nodes of the input graph and $\Delta$ is its maximum degree. This means that randomized…

Data Structures and Algorithms · Computer Science 2022-11-15 Manuela Fischer , Yannic Maus , Magnús M. Halldórsson

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
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