004 Datenverarbeitung; Informatik
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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.
Given points in the plane, connect them using minimum ink. Though the task seems simple, it turns out to be very time consuming. In fact, scientists believe that computers cannot efficiently solve it. So, do we have to resign? This book examines such NP-hard network-design problems, from connectivity problems in graphs to polygonal drawing problems on the plane. First, we observe why it is so hard to optimally solve these problems. Then, we go over to attack them anyway. We develop fast algorithms that find approximate solutions that are very close to the optimal ones. Hence, connecting points with slightly more ink is not hard.
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.