Euclidean Distance Geometry

An Introduction

  • Leo Liberti
  • Carlile Lavor

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Leo Liberti, Carlile Lavor
    Pages 1-8
  3. Leo Liberti, Carlile Lavor
    Pages 9-18
  4. Leo Liberti, Carlile Lavor
    Pages 19-30
  5. Leo Liberti, Carlile Lavor
    Pages 31-42
  6. Leo Liberti, Carlile Lavor
    Pages 43-55
  7. Leo Liberti, Carlile Lavor
    Pages 57-65
  8. Leo Liberti, Carlile Lavor
    Pages 67-79
  9. Leo Liberti, Carlile Lavor
    Pages 81-92
  10. Leo Liberti, Carlile Lavor
    Pages 93-96
  11. Back Matter
    Pages 97-133

About this book

Introduction

This textbook, the first of its kind, presents the fundamentals of distance geometry:  theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several.  Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.

Keywords

convex optimization complete graphs discretizability K-laterative graphs Mathematica vertex orders Branch-and-Prune algorithm weighted adjacency matrix mathematical programming graph visualization clock synchronization localization of sensor networks unmanned underwater vehicles Isomap Multidimensional Scaling Dimensionality Reduction

Authors and affiliations

  • Leo Liberti
    • 1
  • Carlile Lavor
    • 2
  1. 1.CNRS LIXÉcole PolytechniquePalaiseauFrance
  2. 2.Department of Applied Mathematics (IMECC-UNICAMP)University of CampinasCampinasBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-60792-4
  • Copyright Information Springer International Publishing Switzerland 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-60791-7
  • Online ISBN 978-3-319-60792-4
  • Series Print ISSN 1867-5506
  • Series Online ISSN 1867-5514
  • About this book