Realizing Euclidean distance matrices by sphere intersection

International audienceThis paper presents the theoretical properties of an algorithm to find a realization of a (full) n × n Euclidean distance matrix in the smallest possible embedding dimension. Our algorithm performs linearly in n, and quadratically in the minimum embedding dimension, which is an improvement w.r.t. other algorithms

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure