Related papers: Engineering Edge Orientation Algorithms
Many applications rely on time-intensive matrix operations, such as factorization, which can be sped up significantly for large sparse matrices by interpreting the matrix as a sparse graph and computing a node ordering that minimizes the…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
The maximum edge-weight clique problem is to find a clique whose sum of edge-weight is the maximum for a given edge-weighted undirected graph. The problem is NP-hard and some branch-and-bound algorithms have been proposed. In this paper, we…
The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…
Design patterns being applied more and more to solve the software engineering difficulties in the object oriented software design procedures. So, the design pattern detection is widely used by software industries. Currently, many solutions…
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…
The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
Edge perturbation is a basic method to modify graph structures. It can be categorized into two veins based on their effects on the performance of graph neural networks (GNNs), i.e., graph data augmentation and attack. Surprisingly, both…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
In order to have a compact visualization of the order type of a given point set S, we are interested in geometric graphs on S with few edges that unambiguously display the order type of S. We introduce the concept of exit edges, which…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Recently, researchers have extended the concept of matchings to the more general problem of finding $b$-matchings in hypergraphs broadening the scope of potential applications and challenges. The concept of $b$-matchings, where $b$ is a…
We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let $P$ be a set of $n$ points in the plane and let $S$ be a set of…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
We study graph realization problems from a distributed perspective and we study it in the node capacitated clique (NCC) model of distributed computing, recently introduced for representing peer-to-peer networks. We focus on two central…