Related papers: Snapping Graph Drawings to the Grid Optimally

Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for…

Partial edge drawing (PED) is a drawing style for non-planar graphs, in which edges are drawn only partially as pairs of opposing stubs on the respective end-vertices. In a PED, by erasing the central parts of edges, all edge crossings and…

Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…

State-of-the-art Graph Neural Networks (GNNs) have limited scalability with respect to the graph and model sizes. On large graphs, increasing the model depth often means exponential expansion of the scope (i.e., receptive field). Beyond…

Lifelong SLAM considers long-term operation of a robot where already mapped locations are revisited many times in changing environments. As a result, traditional graph-based SLAM approaches eventually become extremely slow due to the…

Node-link diagrams are widely used to facilitate network explorations. However, when using a graph drawing technique to visualize networks, users often need to tune different algorithm-specific parameters iteratively by comparing the…

We introduce and study level-planar straight-line drawings with a fixed number $\lambda$ of slopes. For proper level graphs, we give an $O(n \log^2 n / \log \log n)$-time algorithm that either finds such a drawing or determines that no such…

Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…

We explore various techniques to incorporate grid-like layout conventions into a force-directed, constraint-based graph layout framework. In doing so we are able to provide high-quality layout---with predominantly axis-aligned edges---that…

We show that finding orthogonal grid-embeddings of plane graphs (planar with fixed combinatorial embedding) with the minimum number of bends in the so-called Kandinsky model (which allows vertices of degree $> 4$) is NP-complete, thus…

Lightweight model design has become an important direction in the application of deep learning technology, pruning is an effective mean to achieve a large reduction in model parameters and FLOPs. The existing neural network pruning methods…

Graph Edit Distance (GED) is defined as the minimum cost transformation of one graph into another and is a widely adopted metric for measuring the dissimilarity between graphs. The major problem of GED is that its computation is NP-hard,…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

A monotone drawing of a planar graph $G$ is a planar straight-line drawing of $G$ where a monotone path exists between every pair of vertices of $G$ in some direction. Recently monotone drawings of planar graphs have been proposed as a new…

We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph G = (V,A) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number…

The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph $H$ of a given graph $G$ such that $H$ has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear…

The algorithm of Gutwenger et al. to insert an edge $e$ in linear time into a planar graph $G$ with a minimal number of crossings on $e$, is a helpful tool for designing heuristics that minimize edge crossings in drawings of general graphs.…