Euclidean Distance Geometry

Leo Liberti is a research director at CNRS and a professor at Ecole Polytechnique, France. Professor Liberti’s mathematical and optimization-related research interests are broad and his publications are extensive. In addition to co-authorship of this present textbook, he has co-edited two volumes with Springer: Distance Geometry, © 2013, 978-1-4614-5127-3  and Global Optimization: From Theory to Implementation, © 2008,  978-0-387-28260-2.Carlile Lavor is a Full Professor at the Department of Applied Mathematics, University of Campinas, Campinas, Brazil. His main research interests are related to theory and applications of distance geometry and geometric algebra. In addition to co-authorship of this present textbook, he is co-author of the SpringerBrief Introduction to Distance Geometry Applied to Molecular Geometry, © 2017, 978-3-319-57182-9, and co-editor of Distance Geometry, © 2013, 978-1-4614-5127-3.

“The book under review is an invitation to a field with a subject as old as the ancient Greeks, with relatively new name - Euclidean Distance Geometry (EDG). … The book addresses readers at undergraduate level, researchers and practioners … . The textbook ends with a generous appendix covering all the prerequisites needed for reading the book which are quite modest.” (Martin Lukarevski, zbMATH 1492.51002, 2022)“The authors’ intended audience is undergraduate students. The book is intensely mathematical. It would probably be more suitable for graduate students in mathematics than undergraduates.” (Anthony J. Duben, Computing Reviews, May 14, 2019)“The authors make use of the computing system Mathematica to show step-by step proofs. Aimed at students with a solid foundation in linear algebra, this text would be appropriate for upper-level undergraduates or graduate students.” (J. A. Bakal, Choice, Vol. 55 (12), August, 2018)“This textbook on distance geometry covers some relevant theory with several algorithms presented in Mathematica. … The featured problems explore graph visualization, sensor networks, molecule topology and more. Beginning graduate students and researchers with a suitable foundation in graph, vector, and matrix theory as well as linear algebra will gain from the modeling explorations here.” (Tom Schulte, MAA Reviews, March, 2018)

• 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.