@phdthesis{Zink2024, author = {Zink, Johannes}, title = {Algorithms for Drawing Graphs and Polylines with Straight-Line Segments}, doi = {10.25972/OPUS-35475}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-354756}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2024}, abstract = {Graphs provide a key means to model relationships between entities. They consist of vertices representing the entities, and edges representing relationships between pairs of entities. To make people conceive the structure of a graph, it is almost inevitable to visualize the graph. We call such a visualization a graph drawing. Moreover, we have a straight-line graph drawing if each vertex is represented as a point (or a small geometric object, e.g., a rectangle) and each edge is represented as a line segment between its two vertices. A polyline is a very simple straight-line graph drawing, where the vertices form a sequence according to which the vertices are connected by edges. An example of a polyline in practice is a GPS trajectory. The underlying road network, in turn, can be modeled as a graph. This book addresses problems that arise when working with straight-line graph drawings and polylines. In particular, we study algorithms for recognizing certain graphs representable with line segments, for generating straight-line graph drawings, and for abstracting polylines. In the first part, we first examine, how and in which time we can decide whether a given graph is a stick graph, that is, whether its vertices can be represented as vertical and horizontal line segments on a diagonal line, which intersect if and only if there is an edge between them. We then consider the visual complexity of graphs. Specifically, we investigate, for certain classes of graphs, how many line segments are necessary for any straight-line graph drawing, and whether three (or more) different slopes of the line segments are sufficient to draw all edges. Last, we study the question, how to assign (ordered) colors to the vertices of a graph with both directed and undirected edges such that no neighboring vertices get the same color and colors are ascending along directed edges. Here, the special property of the considered graph is that the vertices can be represented as intervals that overlap if and only if there is an edge between them. The latter problem is motivated by an application in automated drawing of cable plans with vertical and horizontal line segments, which we cover in the second part. We describe an algorithm that gets the abstract description of a cable plan as input, and generates a drawing that takes into account the special properties of these cable plans, like plugs and groups of wires. We then experimentally evaluate the quality of the resulting drawings. In the third part, we study the problem of abstracting (or simplifying) a single polyline and a bundle of polylines. In this problem, the objective is to remove as many vertices as possible from the given polyline(s) while keeping each resulting polyline sufficiently similar to its original course (according to a given similarity measure).}, subject = {Graphenzeichnen}, language = {en} } @phdthesis{Kindermann2016, author = {Kindermann, Philipp}, title = {Angular Schematization in Graph Drawing}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-020-7 (print)}, doi = {10.25972/WUP-978-3-95826-021-4}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-112549}, school = {W{\"u}rzburg University Press}, pages = {184}, year = {2016}, abstract = {Graphs are a frequently used tool to model relationships among entities. A graph is a binary relation between objects, that is, it consists of a set of objects (vertices) and a set of pairs of objects (edges). Networks are common examples of modeling data as a graph. For example, relationships between persons in a social network, or network links between computers in a telecommunication network can be represented by a graph. The clearest way to illustrate the modeled data is to visualize the graphs. The field of Graph Drawing deals with the problem of finding algorithms to automatically generate graph visualizations. The task is to find a "good" drawing, which can be measured by different criteria such as number of crossings between edges or the used area. In this thesis, we study Angular Schematization in Graph Drawing. By this, we mean drawings with large angles (for example, between the edges at common vertices or at crossing points). The thesis consists of three parts. First, we deal with the placement of boxes. Boxes are axis-parallel rectangles that can, for example, contain text. They can be placed on a map to label important sites, or can be used to describe semantic relationships between words in a word network. In the second part of the thesis, we consider graph drawings visually guide the viewer. These drawings generally induce large angles between edges that meet at a vertex. Furthermore, the edges are drawn crossing-free and in a way that makes them easy to follow for the human eye. The third and final part is devoted to crossings with large angles. In drawings with crossings, it is important to have large angles between edges at their crossing point, preferably right angles.}, language = {en} } @phdthesis{Loeffler2021, author = {L{\"o}ffler, Andre}, title = {Constrained Graph Layouts: Vertices on the Outer Face and on the Integer Grid}, edition = {1. Auflage}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-146-4}, doi = {10.25972/WUP-978-3-95826-147-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-215746}, school = {W{\"u}rzburg University Press}, pages = {viii, 161}, year = {2021}, abstract = {Constraining graph layouts - that is, restricting the placement of vertices and the routing of edges to obey certain constraints - is common practice in graph drawing. In this book, we discuss algorithmic results on two different restriction types: placing vertices on the outer face and on the integer grid. For the first type, we look into the outer k-planar and outer k-quasi-planar graphs, as well as giving a linear-time algorithm to recognize full and closed outer k-planar graphs Monadic Second-order Logic. For the second type, we consider the problem of transferring a given planar drawing onto the integer grid while perserving the original drawings topology; we also generalize a variant of Cauchy's rigidity theorem for orthogonal polyhedra of genus 0 to those of arbitrary genus.}, subject = {Graphenzeichnen}, language = {en} } @phdthesis{Fink2014, author = {Fink, Martin}, title = {Crossings, Curves, and Constraints in Graph Drawing}, publisher = {W{\"u}rzburg University Press}, isbn = {978-3-95826-002-3 (print)}, doi = {10.25972/WUP-978-3-95826-003-0}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-98235}, school = {W{\"u}rzburg University Press}, pages = {222}, year = {2014}, abstract = {In many cases, problems, data, or information can be modeled as graphs. Graphs can be used as a tool for modeling in any case where connections between distinguishable objects occur. Any graph consists of a set of objects, called vertices, and a set of connections, called edges, such that any edge connects a pair of vertices. For example, a social network can be modeled by a graph by transforming the users of the network into vertices and friendship relations between users into edges. Also physical networks like computer networks or transportation networks, for example, the metro network of a city, can be seen as graphs. For making graphs and, thereby, the data that is modeled, well-understandable for users, we need a visualization. Graph drawing deals with algorithms for visualizing graphs. In this thesis, especially the use of crossings and curves is investigated for graph drawing problems under additional constraints. The constraints that occur in the problems investigated in this thesis especially restrict the positions of (a part of) the vertices; this is done either as a hard constraint or as an optimization criterion.}, subject = {Graphenzeichnen}, language = {en} } @phdthesis{Kryven2022, author = {Kryven, Myroslav}, title = {Optimizing Crossings in Circular-Arc Drawings and Circular Layouts}, isbn = {978-3-95826-174-7}, doi = {10.25972/WUP-978-3-95826-175-4}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-245960}, school = {Universit{\"a}t W{\"u}rzburg}, pages = {viii, 129}, year = {2022}, abstract = {A graph is an abstract network that represents a set of objects, called vertices, and relations between these objects, called edges. Graphs can model various networks. For example, a social network where the vertices correspond to users of the network and the edges represent relations between the users. To better see the structure of a graph it is helpful to visualize it. The research field of visualizing graphs is called Graph Drawing. A standard visualization is a node-link diagram in the Euclidean plane. In such a representation the vertices are drawn as points in the plane and edges are drawn as Jordan curves between every two vertices connected by an edge. Edge crossings decrease the readability of a drawing, therefore, Crossing Optimization is a fundamental problem in Graph Drawing. Graphs that can be drawn with few crossings are called beyond-planar graphs. The topic that deals with definition and analysis of beyond-planar graphs is called Beyond Planarity and it is an important and relatively new research area in Graph Drawing. In general, beyond planar graphs posses drawings where edge crossings are restricted in some way. For example, the number of crossings may be bounded by a constant independent of the size of the graph. Crossings can also be restricted locally by, for example, restricting the number of crossings per edge, restricting the number of pairwise crossing edges, or bounding the crossing angle of two edges in the drawing from below. This PhD thesis defines and analyses beyond-planar graph classes that arise from such local restrictions on edge crossings.}, subject = {Graphenzeichnen}, language = {en} }