Combinatorial geometry and its algorithmic applications : the Alcalá lectures
著者
書誌事項
Combinatorial geometry and its algorithmic applications : the Alcalá lectures
（Mathematical surveys and monographs, v. 152）
American Mathematical Society, c2009
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注記
"These lecture notes are a compilation of surveys of the topics that were presented in a series of talks at Alcalá, Spain, August 31-September 5, 2006 by János Pach and Micha Sharir. To a large extent, these surveys are adapted from earlier papers written by the speakers and their collaborators"--Pref. and apology
Includes bibliographical references (p. 197-226) and index
内容説明・目次
内容説明
Based on a lecture series given by the authors at a satellite meeting of the 2006 International Congress of Mathematicians and on many articles written by them and their collaborators, this volume provides a comprehensive up-to-date survey of several core areas of combinatorial geometry. It describes the beginnings of the subject, going back to the nineteenth century (if not to Euclid), and explains why counting incidences and estimating the combinatorial complexity of various arrangements of geometric objects became the theoretical backbone of computational geometry in the 1980s and 1990s. The combinatorial techniques outlined in this book have found applications in many areas of computer science from graph drawing through hidden surface removal and motion planning to frequency allocation in cellular networks. ""Combinatorial Geometry and Its Algorithmic Applications"" is intended as a source book for professional mathematicians and computer scientists as well as for graduate students interested in combinatorics and geometry. Most chapters start with an attractive, simply formulated, but often difficult and only partially answered mathematical question, and describes the most efficient techniques developed for its solution. The text includes many challenging open problems, figures, and an extensive bibliography.
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