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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…
Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of $G$ that induces a connected subgraph. In this paper we describe some approaches to solve the CVC problem exactly. First, we give…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of $n$ disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between…
Vertex deletion problems ask whether it is possible to delete at most $k$ vertices from a graph so that the resulting graph belongs to a specified graph class. Over the past years, the parameterized complexity of vertex deletion to a…
Graph filters are one of the core tools in graph signal processing. A central aspect of them is their direct distributed implementation. However, the filtering performance is often traded with distributed communication and computational…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
Evolution of large scale networks demand for efficient way of communication in the networks. One way to propagate information in the network is to find vertex cover. In this paper we describe a variant of vertex cover problem naming it…
We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unified family of controllers, including the classical gradient…
Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal graph needs to have at least $2n-4$ edges…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
The radius and diameter are fundamental graph parameters. They are defined as the minimum and maximum of the eccentricities in a graph, respectively, where the eccentricity of a vertex is the largest distance from the vertex to another…
A dominating set of a graph $\mathcal{G=(V, E)}$ is a subset of vertices $S\subseteq\mathcal{V}$ such that every vertex $v\in \mathcal{V} \setminus S$ outside the dominating set is adjacent to a vertex $u\in S$ within the set. The minimum…
Summarizing large-scaled directed graphs into small-scale representations is a useful but less studied problem setting. Conventional clustering approaches, which based on "Min-Cut"-style criteria, compress both the vertices and edges of the…
We study the Minimum Sum Vertex Cover problem, which asks for an ordering of vertices in a graph that minimizes the total cover time of edges. In particular, n vertices of the graph are visited according to an ordering, and for each edge…
We present a new parameterized algorithm for the {feedback vertex set} problem ({\sc fvs}) on undirected graphs. We approach the problem by considering a variation of it, the {disjoint feedback vertex set} problem ({\sc disjoint-fvs}),…
An instance of the maximum mixed graph orientation problem consists of a mixed graph and a collection of source-target vertex pairs. The objective is to orient the undirected edges of the graph so as to maximize the number of pairs that…
This paper addresses the challenge of object-centric layout generation under spatial constraints, seen in multiple domains including floorplan design process. The design process typically involves specifying a set of spatial constraints…