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Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…

Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…

In this paper, we present a novel workflow consisting of algebraic algorithms and data structures for fast and topologically accurate conversion of vector data models such as Boundary Representations into voxels (topological voxelization);…

Graphs are often used to model relationships between entities. The identification and visualization of clusters in graphs enable insight discovery in many application areas, such as life sciences and social sciences. Force-directed graph…

Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…

Estimating output changes by input changes is the main task in causal analysis. In previous work, input and output Self-Organizing Maps (SOMs) were associated for causal analysis of multivariate and nonlinear data. Based on the association,…

When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…

Prior research has shown that human perception of similarity differs from mathematical measures in visual comparison tasks, including those involving directed acyclic graphs. This divergence can lead to missed differences and skepticism…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

While many graph drawing algorithms consider nodes as points, graph visualization tools often represent them as shapes. These shapes support the display of information such as labels or encode various data with size or color. However, they…

Metro or transit maps, are schematic representations of transit networks to facilitate effective route-finding. These maps are often advertised on a web page or pamphlet highlighting routes from source to destination stations. To visually…

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…

We examine ordered graphs, defined as graphs with linearly ordered vertices, from the perspective of homomorphisms (and colorings) and their complexities. We demonstrate the corresponding computational and parameterized complexities, along…

Communication networks form the backbone of our society. Topology control algorithms optimize the topology of such communication networks. Due to the importance of communication networks, a topology control algorithm should guarantee…

This work proposes a novel hybrid approach for vision-only navigation of mobile robots, which combines advances of both deep learning approaches and classical model-based planning algorithms. Today, purely data-driven end-to-end models are…

We explore the problem of sampling graph signals in scenarios where the graph structure is not predefined and must be inferred from data. In this scenario, existing approaches rely on a two-step process, where a graph is learned first,…

The ability to recognize the position and order of the floor-level lines that divide adjacent building floors can benefit many applications, for example, urban augmented reality (AR). This work tackles the problem of locating floor-level…

This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…