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Related papers: A Note on Hardness of Diameter Approximation

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Network decomposition is a central concept in the study of distributed graph algorithms. We present the first polylogarithmic-round deterministic distributed algorithm with small messages that constructs a strong-diameter network…

Data Structures and Algorithms · Computer Science 2021-06-08 Yi-Jun Chang , Mohsen Ghaffari

The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only $O(log(n))$ bits of information each may be…

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

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

Machine Learning · Computer Science 2023-11-10 Daniel Carmon , Roi Livni , Amir Yehudayoff

In the past few years, a successful line of research has lead to lower bounds for several fundamental local graph problems in the distributed setting. These results were obtained via a technique called round elimination. On a high level,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-29 Alkida Balliu , Sebastian Brandt , Fabian Kuhn , Dennis Olivetti , Joonatan Saarhelo

In this paper we provide a parallel algorithm that given any $n$-node $m$-edge directed graph and source vertex $s$ computes all vertices reachable from $s$ with $\tilde{O}(m)$ work and $n^{1/2 + o(1)}$ depth with high probability in $n$ .…

Data Structures and Algorithms · Computer Science 2019-12-09 Arun Jambulapati , Yang P. Liu , Aaron Sidford

An extremity is a vertex such that the removal of its closed neighbourhood does not increase the number of connected components. Let $Ext_{\alpha}$ be the class of all connected graphs whose quotient graph obtained from modular…

Data Structures and Algorithms · Computer Science 2023-02-28 Guillaume Ducoffe

High order networks are weighted hypergraphs col- lecting relationships between elements of tuples, not necessarily pairs. Valid metric distances between high order networks have been defined but they are difficult to compute when the…

Social and Information Networks · Computer Science 2016-05-04 Weiyu Huang , Alejandro Ribeiro

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$…

Data Structures and Algorithms · Computer Science 2014-05-01 Mohsen Ghaffari

Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between…

Data Structures and Algorithms · Computer Science 2021-11-18 Sebastian Forster , Martin Grösbacher , Tijn de Vos

In the context of communication complexity, we explore protocols for graph coloring, focusing on the vertex and edge coloring problems in $n$-vertex graphs $G$ with a maximum degree $\Delta$. We consider a scenario where the edges of $G$…

Data Structures and Algorithms · Computer Science 2025-05-12 Yi-Jun Chang , Gopinath Mishra , Hung Thuan Nguyen , Farrel D Salim

Token ring topology has been frequently used in the design of distributed loop computer networks and one measure of its performance is the diameter. We propose an algorithm for constructing hamiltonian graphs with $n$ vertices and maximum…

Discrete Mathematics · Computer Science 2011-04-19 Aleksandar Ili\' c , Dragan Stevanovi\' c

In this paper, we provide an $O(n \mathrm{polylog} n)$ bound on the expected complexity of the randomly weighted Voronoi diagram of a set of $n$ sites in the plane, where the sites can be either points, interior-disjoint convex sets, or…

Computational Geometry · Computer Science 2015-03-23 Sariel Har-Peled , Benjamin Raichel

Diameter, radius and eccentricities are fundamental graph parameters, which are extensively studied in various computational settings. Typically, computing approximate answers can be much more efficient compared with computing exact…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-12-08 Bertie Ancona , Keren Censor-Hillel , Mina Dalirrooyfard , Yuval Efron , Virginia Vassilevska Williams

There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…

Data Structures and Algorithms · Computer Science 2016-11-22 Haris Angelidakis , Yury Makarychev , Vsevolod Oparin

As the main contribution of this work we present deterministic edge coloring algorithms in the CONGEST model. In particular, we present an algorithm that edge colors any $n$-node graph with maximum degree $\Delta$ with with…

Data Structures and Algorithms · Computer Science 2026-03-04 Joakim Blikstad , Yannic Maus , Tijn de Vos

We present simple deterministic algorithms for subgraph finding and enumeration in the broadcast CONGEST model of distributed computation: -- For any constant $k$, detecting $k$-paths and trees on $k$ nodes can be done in $O(1)$ rounds. --…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-09-22 Janne H. Korhonen , Joel Rybicki

Finding important nodes in a graph and measuring their importance is a fundamental problem in the analysis of social networks, transportation networks, biological systems, etc. Among popular such metrics are graph centrality, betweenness…

Data Structures and Algorithms · Computer Science 2017-04-21 Søren Dahlgaard , Jacob Evald

Algorithmic meta-theorems, stating that graph properties expressible in some particular logic can be decided efficiently in graph classes having some specific structural properties, are now standard in sequential graph algorithms. One of…

Data Structures and Algorithms · Computer Science 2025-07-16 Benjamin Jauregui , Jason Li , Pedro Montealegre , Ioan Todinca

Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are…

Optimization and Control · Mathematics 2021-06-25 Emily A. Reed , Guilherme Ramos , Paul Bogdan , Sérgio Pequito