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 consist of an incomplete …

The problem of protein structure prediction (PSP) represents one of the most important
challenges in computational biology. Determining the three dimensional structure of proteins …

What do clocks, wireless devices, atoms, and submarines have in common? They move: the
clocks move time forward (so to speak), wireless devices usually move on a plane (like an …

We discuss a discretization-based solution approach for a classic problem in global
optimization, namely the distance geometry problem (DGP). We focus our attention on a …

We introduce the discretizable distance geometry problem in R^ 3 (DDGP 3), which consists
in a subclass of instances of the Distance Geometry Problem for which an embedding in R …

Given a weighted, undirected simple graph G=(V, E, d)(where d: E → R _+), the distance
geometry problem (DGP) is to determine an embedding x: V → R^ K such that ∀ {i, j\} ∈ E\; …

When a weighted graph is an instance of the Distance Geometry Problem (DGP), certain
types of vertex orders (called discretization orders) allow the use of a very efficient, precise …

Euclidean distance embedding appears in many high-profile applications including wireless
sensor network localization, where not all pairwise distances among sensors are known or …

This book offers a gentle introduction to key elements of Geometric Algebra, along with their
applications in Physics, Robotics and Molecular Geometry. Major applications covered are …

Abstract Nuclear Magnetic Resonance (NMR) experiments provide distances between
nearby atoms of a protein molecule. The corresponding structure determination problem is …