Algorithms and Computation in Mathematics

Triangulations

Structures for Algorithms and Applications

Authors: De Loera, Jesus, Rambau, Joerg, Santos, Francisco

  • First comprehensive treatment of the theory of regular triangulations, secondary polytopes and related topics appearing in book form
  • Discusses the geometric structure behind the algorithms and shows new emerging applications
  • Theory discusses high-dimensional situations, an area that is not always covered in computational geometry
  • Step-by-step introduction assuming very little background
  • Hundreds of illustrations, examples, and exercises
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eBook $64.99
price for USA (gross)
  • ISBN 978-3-642-12971-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-3-642-12970-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Triangulations appear everywhere, from volume computations and meshing to algebra and topology. This book studies the subdivisions and triangulations of polyhedral regions and point sets and presents the first comprehensive treatment of the theory of secondary polytopes and related topics. A central theme of the book is the use of the rich structure of the space of triangulations to solve computational problems (e.g., counting the number of triangulations or finding optimal triangulations with respect to various criteria), and to establish connections to applications in algebra, computer science, combinatorics, and optimization. With many examples and exercises, and with nearly five hundred illustrations, the book gently guides readers through the properties of the spaces of triangulations of "structured" (e.g., cubes, cyclic polytopes, lattice polytopes) and "pathological" (e.g., disconnected spaces of triangulations) situations using only elementary principles.

About the authors

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".

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)

“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 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.” (Matthias Beck, Zentralblatt MATH, Vol. 1207, 2011)


Table of contents (9 chapters)

  • Triangulations in Mathematics

    Loera, Jesús A. (et al.)

    Pages 1-41

  • Configurations, Triangulations, Subdivisions, and Flips

    Loera, Jesús A. (et al.)

    Pages 43-92

  • Life in Two Dimensions

    Loera, Jesús A. (et al.)

    Pages 93-148

  • A Tool Box

    Loera, Jesús A. (et al.)

    Pages 149-208

  • Regular Triangulations and Secondary Polytopes

    Loera, Jesús A. (et al.)

    Pages 209-274

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-3-642-12971-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-3-642-12970-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Triangulations
Book Subtitle
Structures for Algorithms and Applications
Authors
Series Title
Algorithms and Computation in Mathematics
Series Volume
25
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-12971-1
DOI
10.1007/978-3-642-12971-1
Hardcover ISBN
978-3-642-12970-4
Series ISSN
1431-1550
Edition Number
1
Number of Pages
XIII, 535
Topics