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This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Data Structures and Algorithms · Computer Science 2013-09-25 Vincent Blondel , Kyomin Jung , Pushmeet Kohli , Devavrat Shah

We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…

Data Structures and Algorithms · Computer Science 2022-08-19 Zeev Nutov

We study an NP-hard problem motivated by energy-efficiently maintaining the connectivity of a symmetric wireless communication network: Given an edge-weighted $n$-vertex graph, find a connected spanning subgraph of minimum cost, where the…

Data Structures and Algorithms · Computer Science 2022-03-23 Matthias Bentert , René van Bevern , André Nichterlein , Rolf Niedermeier , Pavel V. Smirnov

A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…

Data Structures and Algorithms · Computer Science 2017-11-28 Krishnendu Chatterjee , Wolfgang Dvořák , Monika Henzinger , Veronika Loitzenbauer

Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…

Networking and Internet Architecture · Computer Science 2015-03-20 Xiaohua Xu , Xiang-Yang Li

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al.…

Discrete Mathematics · Computer Science 2022-07-07 Ozan Heydt , Simeon Kublenz , Patrice Ossona de Mendez , Sebastian Siebertz , Alexandre Vigny

The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…

Computational Geometry · Computer Science 2023-02-21 Sujoy Bhore , Robert Ganian , Liana Khazaliya , Fabrizio Montecchiani , Martin Nöllenburg

We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-02-09 Matteo Ceccarello , Andrea Pietracaprina , Geppino Pucci , Eli Upfal

In the Connected Dominating Set problem we are given a graph $G=(V,E)$ and seek a minimum size dominating set $S \subseteq V$ such that the subgraph $G[S]$ of $G$ induced by $S$ is connected. In the $2$-Edge-Connected Dominating Set problem…

Data Structures and Algorithms · Computer Science 2019-12-23 Amir Belgi , Zeev Nutov

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph. The minimum weight efficient domination problem is the problem of finding an efficient…

Discrete Mathematics · Computer Science 2014-11-26 Andreas Brandstädt , Pavel Fičur , Arne Leitert , Martin Milanič

We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…

Data Structures and Algorithms · Computer Science 2019-08-12 Hiroshi Eto , Tesshu Hanaka , Yasuaki Kobayashi , Yusuke Kobayashi

A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…

Data Structures and Algorithms · Computer Science 2014-02-07 Guilherme D. da Fonseca , Celina M. H. de Figueiredo , Vinícius G. P. de Sá , Raphael Machado

In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…

Data Structures and Algorithms · Computer Science 2012-03-01 Marek Cygan

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

A mixed dominating set is a collection of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for \textsc{Mixed Dominating Set}, resolving some open questions.…

Data Structures and Algorithms · Computer Science 2023-06-22 Louis Dublois , Michael Lampis , Vangelis Th. Paschos

We investigate graph problems in the following setting: we are given a graph $G$ and we are required to solve a problem on $G^2$. While we focus mostly on exploring this theme in the distributed CONGEST model, we show new results and…

Data Structures and Algorithms · Computer Science 2020-06-09 Reuven Bar-Yehuda , Keren Censor-Hillel , Yannic Maus , Shreyas Pai , Sriram V. Pemmaraju

We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…

Data Structures and Algorithms · Computer Science 2016-04-21 Fedor V. Fomin , Daniel Lokshtanov , Dániel Marx , Marcin Pilipczuk , Michał Pilipczuk , Saket Saurabh

A set $D\subseteq V$ of a graph $G=(V,E)$ is called a restrained dominating set of $G$ if every vertex not in $D$ is adjacent to a vertex in $D$ and to a vertex in $V \setminus D$. The \textsc{Minimum Restrained Domination} problem is to…

Discrete Mathematics · Computer Science 2016-06-09 Arti Pandey , B. S. Panda

The k-domination number of a graph is the minimum size of a set X such that every vertex of G is in distance at most k from X. We give a linear time constant-factor approximation algorithm for k-domination number in classes of graphs with…

Combinatorics · Mathematics 2011-10-25 Zdenek Dvorak