Overview

"Triangulations appear in many different parts of mathematics and computer science since they are the natural way to decompose a region of space into smaller, easy-to-handle pieces. From volume computations and meshing to algebra and topology, there are many natural situations in which one has a ?xed set of points that can be used as vertices for the triangulation. Typically one wants to ?nd an optimal triangulation of those points or to explore the set of their all triangulations. The given points may represent the ""sites"" for a Delaunay triangulation computation, d thetest pointsfora surfacereconstruction,ora set ofmonomials,representedaslattice pointsinZ ,inanalgebra- geometric meaning. A central theme of this book is to use the rich geometric structure of the space of triangulations of a given set of points to solve computational problems (e.g., counting the number of triangulations or ?nding optimal triangulations with respect to various criteria), and for setting up connections to novel applications in algebra, computer science, combinatorics, and optimization. Thus at the heart of the book is a comprehensive treatment of the theory of regular subdivisions, secondary polytopes, ?ips, chambers, and their interactions. Again, we ?rmly believe that understandingthe fundamentsof geometry and combinatoricspays up for algorithmsand applications."

Full Product Details

Author:   Jesus De Loera ,  Joerg Rambau ,  Francisco Santos ,  Jesus A De Loera
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   25
Dimensions:   Width: 19.30cm , Height: 2.80cm , Length: 26.00cm
Weight:   1.632kg
ISBN:  

9783642129704

ISBN 10:   3642129706
Pages:   535
Publication Date:   06 September 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Triangulations in Mathematics.- Configurations, Triangulations, Subdivisions, and Flips.- Life in Two Dimensions.- A Tool Box.- Regular Triangulations and Secondary Polytopes.- Some Interesting Configurations.- Some Interesting Triangulations.- Algorithmic Issues.- Further Topics.

Reviews

From the reviews: Focusing on the structure of the set of all possible triangulations ! the current study sits at the threshold of geometry and combinatorics ! . offering terra firma to students still struggling with abstraction, the central theorem ! only dates to 1989, so the present elaboration carries readers to the frontiers of research. ! It is unusual to find such a leisurely, generous exposition of a new subject, as replete with illustrations as contemporary calculus textbooks. ! Summing Up: Recommended. Upper-division undergraduates through professionals. (D. V. Feldman, Choice, Vol. 49 (1), September, 2011)

Author Information

"J.A. De Loera is a professor of mathematics at the University of California, Davis. His work approaches difficult computational problems in discrete mathematics and optimization using tools from algebra and convex geometry. His research has been recognized by an Alexander von Humboldt Fellowship and several national and international grants. He is an associate editor of the journal ""Discrete Optimization"". Jörg Rambau is the chair professor of Wirtschaftsmathematik (Business Mathematics) at the Universität of Bayreuth since 2004. Before that he was associate head of the optimization department at the Zuse Institute Berlin (ZIB). His research encompasses problems in applied optimization, algorithmic discrete mathematics and combinatorial geometry. He is the creator of the state of the art program for triangulation computations TOPCOM. He is associate editor of the ""Jahresberichte der Deutschen Mathematiker-Vereinigung"". Francisco Santos, a professor at the Universidad de Cantabria Spain, received the Young Researcher award from the Universidad Complutense de Madrid in 2003 and was an invited speaker in the Combinatorics Section of the International Congress of Mathematicians in 2006. He is well-known for his explicit constructions of polytopes with disconnected spaces of triangulations, some of which are featured in this book. He is an editor of Springer Verlag's journal ""Discrete and Computational Geometry""."

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