相关论文: Geometric Simultaneous RAC Drawings of Graphs
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…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
We consider the problem of placing arrow heads in directed graph drawings without them overlapping other drawn objects. This gives drawings where edge directions can be deduced unambiguously. We show hardness of the problem, present exact…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…
In this short note, we show two NP-completeness results regarding the \emph{simultaneous representation problem}, introduced by Lubiw and Jampani. The simultaneous representation problem for a given class of intersection graphs asks if some…
A graph G is an a-angle crossing (aAC) graph if every pair of crossing edges in G intersect at an angle of at least a. The concept of right angle crossing (RAC) graphs (a=Pi/2) was recently introduced by Didimo et. al. It was shown that any…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An…
A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been…
This work introduces a multidimensional generalization of the maximum bisection problem. A mixed integer linear programming formulation is proposed with the proof of its correctness. The numerical tests, made on the randomly generated…
In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
There have been extensive works dealing with genetic algorithms (GAs) for seeking optimal solutions of shop scheduling problems. Due to the NP hardness, the time cost is always heavy. With the development of high performance computing (HPC)…
Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these…