Related papers: Greedy domination on biclique-free graphs
We study adaptive greedy algorithms for the problems of stochastic set cover with perfect and imperfect coverages. In stochastic set cover with perfect coverage, we are given a set of items and a ground set B. Evaluating an item reveals its…
We study the influence minimization problem: given a graph $G$ and a seed set $S$, blocking at most $b$ nodes or $b$ edges such that the influence spread of the seed set is minimized. This is a pivotal yet underexplored aspect of network…
Given a graph $G = (V, E)$, a set $S \subseteq V \cup E$ of vertices and edges is called a mixed dominating set if every vertex and edge that is not included in $S$ happens to be adjacent or incident to a member of $S$. The mixed domination…
In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…
A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ admits a perfect matching. The minimum cardinality of a paired dominating set of $G$ is…
In this work, we study online graph problems with monotone-sum objectives. We propose a general two-fold greedy algorithm that references yardstick algorithms to achieve $t$-competitiveness while incurring at most…
The random greedy algorithm for constructing a large partial Steiner-Triple-System is defined as follows. We begin with a complete graph on $n$ vertices and proceed to remove the edges of triangles one at a time, where each triangle removed…
Counting dominating sets in a graph $G$ is closely related to the neighborhood complex of $G$. We exploit this relation to prove that the number of dominating sets $d(G)$ of a graph is determined by the number of complete bipartite…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
Directed graphs provide more subtle and precise modelling tools for optimization in road networks than simple graphs. In particular, they are more suitable in the context of alternative fuel vehicles and new automotive technologies, like…
We analyse the size of an independent set in a random graph on $n$ vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent…
Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and…
The dynamic set cover problem has been subject to growing research attention in recent years. In this problem, we are given as input a dynamic universe of at most $n$ elements and a fixed collection of $m$ sets, where each element appears…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
Kernel-based schemes are state-of-the-art techniques for learning by data. In this work we extend some ideas about kernel-based greedy algorithms to exponential-polynomial splines, whose main drawback consists in possible overfitting and…
Let ${[n] \choose k}$ and ${[n] \choose l}$ $( k > l ) $ where $[n] = \{1,2,3,...,n\}$ denote the family of all $k$-element subsets and $l$-element subsets of $[n]$ respectively. Define a bipartite graph $G_{k,l} = ({[n] \choose k},{[n]…
A set of vertices $W$ of a graph $G$ is a total $k$-dominating set when every vertex of $G$ has at least $k$ neighbors in $W$. In a recent article, Chiarelli et al.\ (Improved Algorithms for $k$-Domination and Total $k$-Domination in Proper…
In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and…
The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is…