Euclidean distance geometry : an introduction

Abstract

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. Introduction -- 1. Motivation -- 2. The Distance Geometry Problem -- 3. Realizing Complete Graphs -- 4. Discretizability -- 5. Molecular Distance Geometry Problems -- 6. Vertex Orders -- 7. Flexibility and Rigidity -- 8. Approximate Realizations -- 9. Taking DG Further -- Appendix A. Mathematical Notions.