@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{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} } @phdthesis{Schwartges2015, author = {Schwartges, Nadine}, title = {Dynamic Label Placement in Practice}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-115003}, school = {Universit{\"a}t W{\"u}rzburg}, year = {2015}, abstract = {The general map-labeling problem is as follows: given a set of geometric objects to be labeled, or features, in the plane, and for each feature a set of label positions, maximize the number of placed labels such that there is at most one label per feature and no two labels overlap. There are three types of features in a map: point, line, and area features. Unfortunately, one cannot expect to find efficient algorithms that solve the labeling problem optimally. Interactive maps are digital maps that only show a small part of the entire map whereas the user can manipulate the shown part, the view, by continuously panning, zooming, rotating, and tilting (that is, changing the perspective between a top and a bird view). An example for the application of interactive maps is in navigational devices. Interactive maps are challenging in that the labeling must be updated whenever labels leave the view and, while zooming, the label size must be constant on the screen (which either makes space for further labels or makes labels overlap when zooming in or out, respectively). These updates must be computed in real time, that is, the computation must be so fast that the user does not notice that we spend time on the computation. Additionally, labels must not jump or flicker, that is, labels must not suddenly change their positions or, while zooming out, a vanished label must not appear again. In this thesis, we present efficient algorithms that dynamically label point and line features in interactive maps. We try to label as many features as possible while we prohibit labels that overlap, jump, and flicker. We have implemented all our approaches and tested them on real-world data. We conclude that our algorithms are indeed real-time capable.}, subject = {Computerkartografie}, 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{Peng2019, author = {Peng, Dongliang}, title = {An Optimization-Based Approach for Continuous Map Generalization}, edition = {1. Auflage}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-104-4}, doi = {10.25972/WUP-978-3-95826-105-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-174427}, school = {W{\"u}rzburg University Press}, pages = {xv, 132}, year = {2019}, abstract = {Maps are the main tool to represent geographical information. Geographical information is usually scale-dependent, so users need to have access to maps at different scales. In our digital age, the access is realized by zooming. As discrete changes during the zooming tend to distract users, smooth changes are preferred. This is why some digital maps are trying to make the zooming as continuous as they can. The process of producing maps at different scales with smooth changes is called continuous map generalization. In order to produce maps of high quality, cartographers often take into account additional requirements. These requirements are transferred to models in map generalization. Optimization for map generalization is important not only because it finds optimal solutions in the sense of the models, but also because it helps us to evaluate the quality of the models. Optimization, however, becomes more delicate when we deal with continuous map generalization. In this area, there are requirements not only for a specific map but also for relations between maps at difference scales. This thesis is about continuous map generalization based on optimization. First, we show the background of our research topics. Second, we find optimal sequences for aggregating land-cover areas. We compare the A\$^{\!\star}\$\xspace algorithm and integer linear programming in completing this task. Third, we continuously generalize county boundaries to provincial boundaries based on compatible triangulations. We morph between the two sets of boundaries, using dynamic programming to compute the correspondence. Fourth, we continuously generalize buildings to built-up areas by aggregating and growing. In this work, we group buildings with the help of a minimum spanning tree. Fifth, we define vertex trajectories that allow us to morph between polylines. We require that both the angles and the edge lengths change linearly over time. As it is impossible to fulfill all of these requirements simultaneously, we mediate between them using least-squares adjustment. Sixth, we discuss the performance of some commonly used data structures for a specific spatial problem. Seventh, we conclude this thesis and present open problems.}, subject = {Generalisierung }, language = {en} } @phdthesis{Fleszar2018, author = {Fleszar, Krzysztof}, title = {Network-Design Problems in Graphs and on the Plane}, edition = {1. Auflage}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-076-4 (Print)}, doi = {10.25972/WUP-978-3-95826-077-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-154904}, school = {W{\"u}rzburg University Press}, pages = {xi, 204}, year = {2018}, abstract = {A network design problem defines an infinite set whose elements, called instances, describe relationships and network constraints. It asks for an algorithm that, given an instance of this set, designs a network that respects the given constraints and at the same time optimizes some given criterion. In my thesis, I develop algorithms whose solutions are optimum or close to an optimum value within some guaranteed bound. I also examine the computational complexity of these problems. Problems from two vast areas are considered: graphs and the Euclidean plane. In the Maximum Edge Disjoint Paths problem, we are given a graph and a subset of vertex pairs that are called terminal pairs. We are asked for a set of paths where the endpoints of each path form a terminal pair. The constraint is that any two paths share at most one inner vertex. The optimization criterion is to maximize the cardinality of the set. In the hard-capacitated k-Facility Location problem, we are given an integer k and a complete graph where the distances obey a given metric and where each node has two numerical values: a capacity and an opening cost. We are asked for a subset of k nodes, called facilities, and an assignment of all the nodes, called clients, to the facilities. The constraint is that the number of clients assigned to a facility cannot exceed the facility's capacity value. The optimization criterion is to minimize the total cost which consists of the total opening cost of the facilities and the total distance between the clients and the facilities they are assigned to. In the Stabbing problem, we are given a set of axis-aligned rectangles in the plane. We are asked for a set of horizontal line segments such that, for every rectangle, there is a line segment crossing its left and right edge. The optimization criterion is to minimize the total length of the line segments. In the k-Colored Non-Crossing Euclidean Steiner Forest problem, we are given an integer k and a finite set of points in the plane where each point has one of k colors. For every color, we are asked for a drawing that connects all the points of the same color. The constraint is that drawings of different colors are not allowed to cross each other. The optimization criterion is to minimize the total length of the drawings. In the Minimum Rectilinear Polygon for Given Angle Sequence problem, we are given an angle sequence of left (+90°) turns and right (-90°) turns. We are asked for an axis-parallel simple polygon where the angles of the vertices yield the given sequence when walking around the polygon in counter-clockwise manner. The optimization criteria considered are to minimize the perimeter, the area, and the size of the axis-parallel bounding box of the polygon.}, subject = {Euklidische Ebene}, 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{Budig2018, author = {Budig, Benedikt}, title = {Extracting Spatial Information from Historical Maps: Algorithms and Interaction}, edition = {1. Auflage}, publisher = {W{\"u}rzburg University Press}, address = {W{\"u}rzburg}, isbn = {978-3-95826-092-4}, doi = {10.25972/WUP-978-3-95826-093-1}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-160955}, school = {W{\"u}rzburg University Press}, pages = {viii, 160}, year = {2018}, abstract = {Historical maps are fascinating documents and a valuable source of information for scientists of various disciplines. Many of these maps are available as scanned bitmap images, but in order to make them searchable in useful ways, a structured representation of the contained information is desirable. This book deals with the extraction of spatial information from historical maps. This cannot be expected to be solved fully automatically (since it involves difficult semantics), but is also too tedious to be done manually at scale. The methodology used in this book combines the strengths of both computers and humans: it describes efficient algorithms to largely automate information extraction tasks and pairs these algorithms with smart user interactions to handle what is not understood by the algorithm. The effectiveness of this approach is shown for various kinds of spatial documents from the 16th to the early 20th century.}, subject = {Karte}, language = {en} }