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Related papers: Lower Bounds for Local Approximation

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We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of…

Data Structures and Algorithms · Computer Science 2018-08-07 Marco Bressan , Enoch Peserico , Luca Pretto

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

We introduce the \emph{local information cost} (LIC), which quantifies the amount of information that nodes in a network need to learn when solving a graph problem. We show that the local information cost presents a natural lower bound on…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-01-23 Peter Robinson

The densest subgraph problem, introduced in the 80s by Picard and Queyranne as well as Goldberg, is a classic problem in combinatorial optimization with a wide range of applications. The lowest outdegree orientation problem is known to be…

Data Structures and Algorithms · Computer Science 2022-09-13 Hsin-Hao Su , Hoa T. Vu

Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…

Data Structures and Algorithms · Computer Science 2018-05-29 Bernhard Haeupler , Jason Li , Goran Zuzic

We study the Densest Subgraph (DSG) problem under the additional constraint of differential privacy. DSG is a fundamental theoretical question which plays a central role in graph analytics, and so privacy is a natural requirement. All known…

Data Structures and Algorithms · Computer Science 2024-04-09 Michael Dinitz , Satyen Kale , Silvio Lattanzi , Sergei Vassilvitskii

$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…

Data Structures and Algorithms · Computer Science 2023-03-29 Mohsen Ghaffari , Christoph Grunau

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…

Data Structures and Algorithms · Computer Science 2016-12-13 Monika Henzinger , Sebastian Krinninger , Danupon Nanongkai

The problem of finding a minimum-weight connected dominating set (CDS) of a given undirected graph has been studied actively, motivated by operations of wireless ad hoc networks. In this paper, we formulate a new stochastic variant of the…

Data Structures and Algorithms · Computer Science 2020-01-01 Takuro Fukunaga

For a well-studied family of domination-type problems, in bounded-treewidth graphs, we investigate whether it is possible to find faster algorithms. For sets $\sigma,\rho$ of non-negative integers, a $(\sigma,\rho)$-set of a graph $G$ is a…

Computational Complexity · Computer Science 2023-06-07 Jacob Focke , Dániel Marx , Fionn Mc Inerney , Daniel Neuen , Govind S. Sankar , Philipp Schepper , Philip Wellnitz

Graph Balancing is the problem of orienting the edges of a weighted multigraph so as to minimize the maximum weighted in-degree. Since the introduction of the problem the best algorithm known achieves an approximation ratio of $1.75$ and it…

Data Structures and Algorithms · Computer Science 2018-11-05 Klaus Jansen , Lars Rohwedder

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…

Performance · Computer Science 2024-01-10 Wenkai Dai , Michael Dinitz , Klaus-Tycho Foerster , Long Luo , Stefan Schmid

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…

Combinatorics · Mathematics 2021-07-08 Étienne Bamas , Louis Esperet

It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-05-15 Ken-ichi Kawarabayashi , Gregory Schwartzman

For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class…

Data Structures and Algorithms · Computer Science 2020-02-24 Fedor V. Fomin , Petr A. Golovach , Jean-Florent Raymond

Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…

Probability · Mathematics 2022-09-07 Remco van der Hofstad , Pim van der Hoorn , Neeladri Maitra

A set $D \subseteq V$ is a dominating set of a graph $G$ if every vertex in $V - D$ is adjacent to at least one vertex in $D$. A dominating set $D$ is a paired-dominating set if the subgraph of $G$ induced by $D$ contains a perfect…

Data Structures and Algorithms · Computer Science 2025-02-25 Ta-Yu Mu , Ching-Chi Lin

We analyze the query complexity of finding a local minimum in $t$ rounds on general graphs. More precisely, given a graph $G = (V,E)$ and oracle access to an unknown function $f : V \to \mathbb{R}$, the goal is to find a local minimum--a…

Computational Complexity · Computer Science 2026-02-03 Simina Brânzei , Ioannis Panageas , Dimitris Paparas

We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected…

Data Analysis, Statistics and Probability · Physics 2023-10-25 Yusupjan Habibulla , Hai-Jun Zhou

An edge of a graph dominates itself along with any edge that shares an endpoint with it. An efficient edge dominating set (also called a dominating induced matching, DIM) is a subset of edges such that each edge of the graph is dominated by…

Combinatorics · Mathematics 2026-03-06 Luciano N. Grippo , Min Chih Lin , Camilo Vera