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Mathematical Surveys and Monographs
2011; 362 pp; hardcover
List Price: US$98
Member Price: US$78.40
Order Code: SURV/173
Combinatorial Geometry and Its Algorithmic Applications: The Alcalá Lectures - Janos Pach and Micha Sharir
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts.
This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Graduate students and research mathematicians interested in the theory and practice of computational geometry.
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