Mucherino A., Lavor C., Liberti L., Maculan N. (Eds.) Distance Geometry: Theory, Methods, and Applications

Springer Science+Business Media, New York, 2013. — 427 p. — ISBN: 1461451272.This volume is a collection of research surveys on the Distance Geometry Problem (DGP) and its applications. It will be divided into three parts: Theory, Methods and Applications. Each part will contain at least one survey and several research papers.
The first part, Theory, will deal with theoretical aspects of the DGP, including a new class of problems and the study of its complexities as well as the relation between DGP and other related topics, such as: distance matrix theory, Euclidean distance matrix completion problem, multispherical structure of distance matrices, distance geometry and geometric algebra, algebraic distance geometry theory, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP: symmetry and complexity.
The second part, Methods, will discuss mathematical and computational properties of methods developed to the problems considered in the first chapter including continuous methods (based on Gaussian and hyperbolic smoothing, difference of convex functions, semidefinite programming, branch-and-bound), discrete methods (based on branch-and-prune, geometric build-up, graph rigidity), and also heuristics methods (based on simulated annealing, genetic algorithms, tabu search, variable neighborhood search).
Applications will comprise the third part and will consider applications of DGP to NMR structure calculation, rational drug design, molecular dynamics simulations, graph drawing and sensor network localization.
This volume will be the firstedited book on distance geometry and applications. The editors are in correspondence with the major contributors to the field of distance geometry, including important research centers in molecular biology such as Institut Pasteur in Paris.Theory
Universal Rigidity of Bar Frameworks in General Position: A Euclidean Distance Matrix Approach
Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs
The Discretizable Molecular Distance Geometry Problem seems Easier on Proteins
Spheres Unions and Intersections and Some of their Applications in Molecular Modeling
Is the Distance Geometry Problem in NP?
Solving Spatial Constraints with Generalized Distance Geometry
A Topological Interpretation of the Walk Distances
Methods
Distance Geometry Methods for Protein Structure Determination
Solving the Discretizable Molecular Distance Geometry Problem by Multiple Realization Trees
ASAP: An Eigenvector Synchronization Algorithm for the Graph Realization Problem
Global Optimization for Atomic Cluster Distance Geometry Problems
Solving Molecular Distance Geometry Problems Using a Continuous Optimization Approach
DC Programming Approaches for Distance Geometry Problems
Stochastic Proximity Embedding: A Simple, Fast and Scalable Algorithm for Solving the Distance Geometry Problem
Applications to Protein Conformations
Distance Geometry for Realistic Molecular Conformations
Distance Geometry in Structural Biology: New Perspectives
Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems
An Overview on Protein Structure Determination by NMR: Historical and Future Perspectives of the use of Distance Geometry Methods