Related papers: A Generalization of Distance Domination

Reachability and shortest path problems are NL-complete for general graphs. They are known to be in L for graphs of tree-width 2 [JT07]. However, for graphs of tree-width larger than 2, no bound better than NL is known. In this paper, we…

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in…

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order $n$ with fixed domination…

A dominating set of a graph $G$ is a set of vertices $D$ such that for all $v \in V(G)$, either $v \in D$ or $(v,d) \in E(G)$ for some $d \in D$. The cardinality redundance of a vertex set $S$, $CR(S)$, is the number of vertices in $V(G)$…

One of the most fundamental problems in wireless networks is to achieve high throughput. Fractional Connected Dominating Set (FCDS) Packings can achieve a throughput of ${\Theta}(k/\log n)$ messages for networks with node connectivity $k$,…

In a vertex-colored graph $G = (V, E)$, a subset $S \subseteq V$ is said to be consistent if every vertex has a nearest neighbor in $S$ with the same color. The problem of computing a minimum cardinality consistent subset of a graph is…

Given a trajectory $T$ and a distance $\Delta$, we wish to find a set $C$ of curves of complexity at most $\ell$, such that we can cover $T$ with subcurves that each are within Fr\'echet distance $\Delta$ to at least one curve in $C$. We…

A dominating set of a graph $G$ is a set $D\subseteq V_G$ such that every vertex in $V_G-D$ is adjacent to at least one vertex in $D$, and the domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. A set…

Mobile guards on the vertices of a graph are used to defend the graph against an infinite sequence of attacks on vertices. A guard must move from a neighboring vertex to an attacked vertex (we assume attacks happen only at vertices…

In this article, we study the $d$-distance $m$-tuple ($\ell, r$)-domination problem. Given a simple undirected graph $G=(V, E)$, and positive integers $d, m, \ell$ and $r$, a subset $V' \subseteq V$ is said to be a $d$-distance $m$-tuple…

A set of vertices $X\subseteq V(G)$ is a $d$-distance dominating set if for every $u\in V(G)\setminus X$ there exists $x\in X$ such that $d(u,x) \le d$, and $X$ is a $p$-packing if $d(u,v) \ge p+1$ for every different $u,v\in X$. The…

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between…

A locating-dominating set is a subset of vertices representing "detectors" in a graph G; each detector monitors its closed neighborhood and can distinguish its own location from its neighbors, and given all sensor input, the system can…

Let $G=(V,E)$ be a graph and $p$ a positive integer. The $p$-domination number $\g_p(G)$ is the minimum cardinality of a set $D\subseteq V$ with $|N_G(x)\cap D|\geq p$ for all $x\in V\setminus D$. The $p$-reinforcement number $r_p(G)$ is…

The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient param-eterized algorithms, this method…

Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…

We present a method for reducing the treewidth of a graph while preserving all of its minimal $s-t$ separators up to a certain fixed size $k$. This technique allows us to solve $s-t$ Cut and Multicut problems with various additional…

Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $S\subseteq V$ such that every vertex not in $S$ is adjacent to at least one vertex in $S$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is…

Clique clustering is the problem of partitioning the vertices of a graph into disjoint clusters, where each cluster forms a clique in the graph, while optimizing some objective function. In online clustering, the input graph is given one…

For a graph G, the k-total dominating graph D_{k}^{t}(G) is the graph whose vertices correspond to the total dominating sets of G that have cardinality at most k; two vertices of D_{k}^{t}(G) are adjacent if and only if the corresponding…