Euclidean Distance Matrices and Their Applications in Rigidity Theory (eBook)

This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. 

​Abdo Y. Alfakih is a Professor in the Department of Mathematics and Statistics at the University of Windsor. He received his PhD in Industrial and Operations Engineering at the University of Michigan. His research interests are in the areas of combinatorial optimization, semidefinite programming. His current work focuses on new approaches to the Graph Realization Problem and its relatives (bar and tensegrity framework rigidity, global rigidity, dimensional rigidity, universal rigidity etc) using Euclidean distance matrices, projected Gram matrices, Gale transform and semidefinite programming.