Triangulations. Structures for algorithms and applications
type: Item
instance of: scholarly article
title: Triangulations. Structures for algorithms and applications
zbMATH Open document ID: 1207.52002
DOI: 10.1007/978-3-642-12971-1
author: Jesús A. De Loera
author: Jörg Rambau
author: Francisco Santos
published in: Algorithms and Computation in Mathematics
publication date: 2010-08-11T00:00:00Z
review text: This book masterfully presents the theory of triangulations of (the convex hull of) a point set alongside many appealing applications in algebra, computer science, combinatorics, and optimization. The authors ``firmly believe that understanding the fundamentals of geometry and combinatorics pays up for algorithms and applications'' of triangulations, and this interplay is beautifully developed. After introductory examples, setting up language and basic constructions, and a concrete chapter on computational geometry in dimension two, the book discusses Gelfand--Kapranov--Zelevinsky's central theorem on secondary polytopes (whose face lattices realize the posets of regular subdivisions of point configurations), followed by important families of configurations and triangulations (e.g., cyclic polytopes, product of simplices, 0/1-polytopes), a chapter on computation and algorithms, and a chapter on further topics (including fiber polytopes, mixed subdivisions, lattice polytopes, Gröbner bases and polytopal complexes). The writing is thorough and engaging, assisted by clear (and numerous) illustrations, and many exercises for the reader. Graduate students and researchers in any area in which triangulations of points set configurations play a role will find this book a comprehensive and most useful reference.
reviewed by: Matthias Beck
Mathematics Subject Classification ID: 52-02
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 52B11
Mathematics Subject Classification ID: 52B45
Mathematics Subject Classification ID: 52B55
Mathematics Subject Classification ID: 68R05
zbMATH DE Number: 5768656
zbMATH Keywords: triangulations
zbMATH Keywords: polyhedral regions
zbMATH Keywords: point set configurations
zbMATH Keywords: volume
zbMATH Keywords: secondary polytope
describes a project that uses: TOPCOM
describes a project that uses: Triangle
describes a project that uses: Gfan
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-12971-1
OpenAlex ID: W4246108584
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description: scientific article; zbMATH DE number 5768656