@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{Atzmueller2006,
author = {Atzm{\"u}ller, Martin},
title = {Knowledge-Intensive Subgroup Mining - Techniques for Automatic and Interactive Discovery},
url = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-21004},
school = {Universit{\"a}t W{\"u}rzburg},
year = {2006},
abstract = {Data mining has proved its significance in various domains and applications. As an important subfield of the general data mining task, subgroup mining can be used, e.g., for marketing purposes in business domains, or for quality profiling and analysis in medical domains. The goal is to efficiently discover novel, potentially useful and ultimately interesting knowledge. However, in real-world situations these requirements often cannot be fulfilled, e.g., if the applied methods do not scale for large data sets, if too many results are presented to the user, or if many of the discovered patterns are already known to the user. This thesis proposes a combination of several techniques in order to cope with the sketched problems: We discuss automatic methods, including heuristic and exhaustive approaches, and especially present the novel SD-Map algorithm for exhaustive subgroup discovery that is fast and effective. For an interactive approach we describe techniques for subgroup introspection and analysis, and we present advanced visualization methods, e.g., the zoomtable that directly shows the most important parameters of a subgroup and that can be used for optimization and exploration. We also describe various visualizations for subgroup comparison and evaluation in order to support the user during these essential steps. Furthermore, we propose to include possibly available background knowledge that is easy to formalize into the mining process. We can utilize the knowledge in many ways: To focus the search process, to restrict the search space, and ultimately to increase the efficiency of the discovery method. We especially present background knowledge to be applied for filtering the elements of the problem domain, for constructing abstractions, for aggregating values of attributes, and for the post-processing of the discovered set of patterns. Finally, the techniques are combined into a knowledge-intensive process supporting both automatic and interactive methods for subgroup mining. The practical significance of the proposed approach strongly depends on the available tools. We introduce the VIKAMINE system as a highly-integrated environment for knowledge-intensive active subgroup mining. Also, we present an evaluation consisting of two parts: With respect to objective evaluation criteria, i.e., comparing the efficiency and the effectiveness of the subgroup discovery methods, we provide an experimental evaluation using generated data. For that task we present a novel data generator that allows a simple and intuitive specification of the data characteristics. The results of the experimental evaluation indicate that the novel SD-Map method outperforms the other described algorithms using data sets similar to the intended application concerning the efficiency, and also with respect to precision and recall for the heuristic methods. Subjective evaluation criteria include the user acceptance, the benefit of the approach, and the interestingness of the results. We present five case studies utilizing the presented techniques: The approach has been successfully implemented in medical and technical applications using real-world data sets. The method was very well accepted by the users that were able to discover novel, useful, and interesting knowledge.},
subject = {Data Mining},
language = {en}
}