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We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$…

In a simple connected graph $G=(V,E)$, a subset of vertices $S \subseteq V$ is a dominating set if any vertex $v \in V\setminus S$ is adjacent to some vertex $x$ from this subset. A number of real-life problems can be modeled using this…

Data Structures and Algorithms · Computer Science 2023-09-04 Ernesto Parra Inza , Frank Angel Hernández Mira , José María Sigarreta Almira , Nodari Vakhania

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

The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and…

Combinatorics · Mathematics 2026-04-08 Dipayan Chakraborty , Florent Foucaud , Aline Parreau , Annegret K. Wagler

In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses $k$-swap as the neighborhood operation. Given a feasible solution $S$, it is the operation…

Data Structures and Algorithms · Computer Science 2019-08-20 Kazuya Haraguchi

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

Data Structures and Algorithms · Computer Science 2017-11-15 Pan Peng , Christian Sohler

A $k$-dominating set is a set $D$ of nodes of a graph such that, for each node $v$, there exists a node $w \in D$ at distance at most $k$ from $v$. Our aim is the deterministic distributed construction of small $T$-dominating sets in time…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-05-04 Avery Miller , Andrzej Pelc

A locating-dominating set $D$ of a graph $G$ is a dominating set of $G$ where each vertex not in $D$ has a unique neighborhood in $D$, and the Locating-Dominating Set problem asks if $G$ contains such a dominating set of bounded size. This…

Data Structures and Algorithms · Computer Science 2023-10-10 Márcia R. Cappelle , Guilherme C. M. Gomes , Vinicius F. dos Santos

A long-standing open question is which graph class is the most general one permitting constant-time constant-factor approximations for dominating sets. The approximation ratio has been bounded by increasingly general parameters such as…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-26 Christoph Lenzen , Sophie Wenning

In this paper we study the special case of Graphic TSP where the underlying graph is a power law graph (PLG). We give a refined analysis of some of the current best approximation algorithms and show that an improved approximation ratio can…

Data Structures and Algorithms · Computer Science 2015-09-15 Mikael Gast , Mathias Hauptmann , Marek Karpinski

In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of B\v{a}doiu,…

Metric Geometry · Mathematics 2015-03-17 Victor Chepoi , Feodor Dragan , Ilan Newman , Yuri Rabinovich , Yann Vaxes

In this work, we initiate a thorough study of parameterized graph optimization problems in the distributed setting. In a parameterized problem, an algorithm decides whether a solution of size bounded by a \emph{parameter} $k$ exists and if…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-08-07 Ran Ben-Basat , Ken-ichi Kawarabayashi , Gregory Schwartzman

The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing…

Computational Complexity · Computer Science 2022-05-03 Faisal Abu-Khzam , Henning Fernau , Benjamin Gras , Mathieu Liedloff , Kevin Mann

We show that for every positive $\epsilon > 0$, unless NP $\subset$ BPQP, it is impossible to approximate the maximum quadratic assignment problem within a factor better than $2^{\log^{1-\epsilon} n}$ by a reduction from the maximum label…

Computational Complexity · Computer Science 2014-04-01 Konstantin Makarychev , Rajsekar Manokaran , Maxim Sviridenko

Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…

Data Structures and Algorithms · Computer Science 2023-07-06 Dongrun Cai , Xue Chen , Pan Peng

In research on distributed local algorithms it is commonly assumed that each vertex has a unique identifier in the entire graph. However, it turns out that in case of certain classes of graphs (for example not lift-closed bounded degree…

Data Structures and Algorithms · Computer Science 2013-03-14 Wojciech Wawrzyniak

We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…

Machine Learning · Computer Science 2022-08-12 Jerome Taupin , Yassir Jedra , Alexandre Proutiere

The $k$-cut problem asks, given a connected graph $G$ and a positive integer $k$, to find a minimum-weight set of edges whose removal splits $G$ into $k$ connected components. We give the first polynomial-time algorithm with approximation…

Data Structures and Algorithms · Computer Science 2018-11-12 MohammadHossein Bateni , Alireza Farhadi , MohammadTaghi Hajiaghayi

A subset $M$ of the edges of a graph $G$ is a matching if no two edges in $M$ are incident. A maximal matching is a matching that is not contained in a larger matching. A subset $S$ of vertices of a graph $G$ with no isolated vertices is a…

Combinatorics · Mathematics 2019-09-09 Selim Bahadır

Given a graph $G=(V,E)$, a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\in E$, there exists a vertex $u\in S$ such that $u$…

Combinatorics · Mathematics 2026-05-12 Yichen Wang , Haixiang Zhang , Mei Lu