Related papers: Hyperbolicity Computation through Dominating Sets
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
$k$-defensive domination, a variant of the classical domination problem on graphs, seeks a minimum cardinality vertex set providing a surjective defense against any attack on vertices of cardinality bounded by a parameter $k$. The problem…
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…
Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…
Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…
The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key…
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 $S$…
Cubicity of a graph $G$ is the smallest dimension $d$, for which $G$ is a unit disc graph in ${\mathbb{R}}^d$, under the $l^\infty$ metric, i.e. $G$ can be represented as an intersection graph of $d$-dimensional (axis-parallel) unit…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
In heterogeneous graphs, we can observe complex structures such as tree-like or hierarchical structures. Recently, the hyperbolic space has been widely adopted in many studies to effectively learn these complex structures. Although these…
The Steiner $k$-eccentricity of a vertex $v$ of a graph $G$ is the maximum Steiner distance over all $k$-subsets of $V (G)$ which contain $v$. A linear time algorithm for calculating the Steiner $k$-eccentricity of a vertex on block graphs…
This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids. The size of the dominating set…
Graph similarity search is among the most important graph-based applications, e.g. finding the chemical compounds that are most similar to a query compound. Graph similarity computation, such as Graph Edit Distance (GED) and Maximum Common…
Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…
Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…
We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…