Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets. This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation. Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.

By presenting state-of-the-art aspects of theoretical computer science and practical applications in various fields, this book commemorates the 60th birthday of Thomas Ottmann. The 26 research papers presented span the whole range of Thomas Ottmann's scientific career, from formal languages to algorithms and data structures, from topics in practical computer science like software engineering or database systems to applications of Web technology, groupware, and e-learning.

This book constitutes the thoroughly refereed post-proceedings of the International Workshop on Sensor Based Intelligent Robots held in Dagstuhl Castle, Germany, in October 2000.The 20 revised full papers were carefully reviewed and improved for inclusion in this book. Addressing a broad variety of aspects of the highly interdisciplinary field of robotics, the book presents three topical sections on sensing, robotics, and intelligence.

The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.

Wie bestimmt man in einer Menge von Punkten am schnellsten zu jedem Punkt seinen nachsten Nachbarn? Wie findet man schnell alle Stadte in einem rechteckigen Kartenausschnitt? Wie misst man die AEhnlichkeit von zwei Kurven?Mit solchen Fragen beschaftigt sich die Algorithmische Geometrie. Dieses Buch gibt eine Einfuhrung in algorithmische Techniken wie Sweep, Divide-and-Conquer, randomisierte inkrementelle Konstruktion, Dynamisierung, amortisierte Kostenanalyse und kompetitive Analyse. Es stellt wichtige geometrische Strukturen, wie konvexe Hulle, Voronoi-Diagramm und Delaunay-Triangulation sowie effiziente Datenstrukturen vor. Diese dritte Auflage wurde grundlich uberarbeitet und erweitert. Sie bietet Dozent*innen die Moeglichkeit, fur Vorlesungen und Seminare eine individuelle Stoffauswahl zu treffen, auch zu weiterfuhrenden Themen wie zum Beispiel ausgewogene hoeherdimensionale Suchbaume, schnelle Triangulierung, Vapnik-Chervonenkis Dimension, AEhnlichkeitsberechnung von Kurven, Bewegungsplanung und Inzidenzen geometrischer Objekte.