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We provide a deterministic CONGEST algorithm to constant factor approximate the minimum dominating set on graphs of bounded arboricity in $O(\log n)$ rounds. This improves over the well-known randomized algorithm of Lenzen and…

Data Structures and Algorithms · Computer Science 2021-02-23 Saeed Akhoondian Amiri

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

Data Structures and Algorithms · Computer Science 2025-12-12 Ryan L. Mann , Gabriel Waite

We give a new randomized distributed algorithm for the $\Delta+1$-list coloring problem. The algorithm and its analysis dramatically simplify the previous best result known of Chang, Li, and Pettie [SICOMP 2020]. This allows for numerous…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-12 Magnús M. Halldórsson , Alexandre Nolin , Tigran Tonoyan

The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just…

Combinatorics · Mathematics 2017-05-08 Anton Bernshteyn

The Lov\'{a}sz Local Lemma (LLL) is a probabilistic tool which shows that, if a collection of "bad" events $\mathcal B$ in a probability space are not too likely and not too interdependent, then there is a positive probability that no…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

Following the groundbreaking Moser-Tardos algorithm for the Lovasz Local Lemma (LLL), a series of works have exploited a key ingredient of the original analysis, the witness tree lemma, in order to: derive deterministic, parallel and…

Discrete Mathematics · Computer Science 2019-06-11 Fotis Iliopoulos

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

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

One of the central models in distributed computing is Linial's LOCAL model [SIAM J. Comp. 1992]. Over time, researchers have studied distributed graph problems in the LOCAL model under slightly different assumptions, such as whether nodes…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-14 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Timothé Picavet , Gustav Schmid

Understanding the role of randomness when solving locally checkable labeling (LCL) problems in the LOCAL model has been one of the top priorities in the research on distributed graph algorithms in recent years. For LCL problems in…

Data Structures and Algorithms · Computer Science 2025-10-27 Sebastian Brandt , Fabian Kuhn , Zahra Parsaeian

We consider recent formulations of the algorithmic Lovasz Local Lemma by Achlioptas-Iliopoulos-Kolmogorov [2] and by Achlioptas-Iliopoulos-Sinclair [3]. These papers analyze a random walk algorithm for finding objects that avoid undesired…

Data Structures and Algorithms · Computer Science 2020-08-17 Vladimir Kolmogorov

The resampling algorithm of Moser \& Tardos is a powerful approach to develop constructive versions of the Lov\'{a}sz Local Lemma (LLL). We generalize this to partial resampling: when a bad event holds, we resample an appropriately-random…

Combinatorics · Mathematics 2023-10-13 David G. Harris , Aravind Srinivasan

Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing,…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-05 Taisuke Izumi , François Le Gall

The Lov\'asz Local Lemma is a powerful probabilistic technique for proving the existence of combinatorial objects. It is especially useful for colouring graphs and hypergraphs with bounded maximum degree. This paper presents a general…

Combinatorics · Mathematics 2021-04-14 Ian M. Wanless , David R. Wood

We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new…

Data Structures and Algorithms · Computer Science 2019-01-16 Heng Guo , Mark Jerrum , Jingcheng Liu

The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…

Computational Complexity · Computer Science 2024-09-20 Shuichi Hirahara , Zhenjian Lu , Mikito Nanashima

The Lenstra-Lenstra-Lovasz (LLL) reduction has wide applications in digital communications. It can greatly improve the speed of the sphere decoding (SD) algorithms for solving an integer least squares (ILS) problem and the performance of…

Information Theory · Computer Science 2012-04-09 Xiaohu Xie , Xiao-Wen Chang , Mazen Al Borno

In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…

Data Structures and Algorithms · Computer Science 2023-07-25 Yi-Jun Chang , Zeyong Li

Distributed vertex coloring is one of the classic problems and probably also the most widely studied problems in the area of distributed graph algorithms. We present a new randomized distributed vertex coloring algorithm for the standard…

Data Structures and Algorithms · Computer Science 2021-04-13 Magnús M. Halldórsson , Fabian Kuhn , Yannic Maus , Tigran Tonoyan

This paper proves that a wide class of local search algorithms extend as is to the fully dynamic setting with an adaptive adversary, achieving an amortized $\tilde{O}(1)$ number of local-search steps per update. A breakthrough by Moser…

Data Structures and Algorithms · Computer Science 2026-04-23 Bernhard Haeupler , Slobodan Mitrović , Srikkanth Ramachandran , Wen-Horng Sheu , Robert Tarjan