Angelika Steger - Böcker

In recent years, algorithmic graph theory has become increasingly important since it serves as a link between discrete mathematics and theoretical computer science. This textbook introduces students of mathematics and computer science to the interrelated fields of graph theory, algorithms and complexity. No specific previous knowledge is assumed. The central theme of the book is a geometrical problem dating back to Jakob Steiner. This problem, now called the Steiner tree problem, was initially of importance only within the context of land surveying. Recent applications, as diverse as VLSI-layout and the study of phylogenetic trees, have, however, lead to significant interest in the problem. The resulting progress has uncovered fascinating connections to and among graph theory, the study of algorithms and complexity. The single problem thus serves to bind and motivate these areas. The book's topics include: exact algorithms; computational complexity; approximation algorithms; limits of approximability; randomness helps; the Manhattan Steiner problem; heuristics; packing of Steiner trees; and applications.A fundamental feature of the book is that each chapter ends with an "excursion" into some related area. These excursions reinforce the concepts and methods introduced for the Steiner tree problem by putting them in a broader context.

Dieses Lehrbuch umfaßt einen Kanon von Themen, der an vielen Universitäten unter dem Titel "Diskrete Strukturen" fester Bestandteil des Informatik-Grundstudiums geworden ist. Bei der Darstellung wird neben der mathematischen Exaktheit besonderer Wert darauf gelegt, auch das intuitive Verständnis zu fördern, um so das Verstehen und Einordnen des Stoffs zu erleichtern. Unterstützt wird dies durch zahlreiche Beispiele und Aufgaben, vorwiegend aus dem Bereich der Informatik. Themen: Kombinatorik, Graphentheorie, Algorithmische Grundprinzipien, Rekursionsgleichungen, Algebra.

During the last few years, we have seen quite spectacular progress in the area of approximation algorithms: for several fundamental optimization problems we now actually know matching upper and lower bounds for their approximability. This textbook-like tutorial is a coherent and essentially self-contained presentation of the enormous recent progress facilitated by the interplay between the theory of probabilistically checkable proofs and aproximation algorithms. The basic concepts, methods, and results are presented in a unified way to provide a smooth introduction for newcomers. These lectures are particularly useful for advanced courses or reading groups on the topic.