Euclidean distance geometry and applications

TL;DR

This paper surveys Euclidean distance geometry, focusing on its theoretical foundations and applications such as molecular conformation, sensor network localization, and statics, emphasizing how incomplete distance data can be used to reconstruct Euclidean points.

Contribution

It provides a comprehensive overview of Euclidean distance geometry theory and highlights key applications in science and engineering.

Findings

Effective methods for reconstructing points from incomplete distances

Applications in molecular conformation and sensor networks

Insights into the theoretical underpinnings of distance-based geometry

Abstract

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.