Euclidean Distance Geometry and Applications

2012/05/02 by Leo Liberti, Liberti, Leo, Carlile Lavor +5 · 250 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Computational Geometry and Mesh Generation #Computer science #Euclidean distance #Euclidean geometry #Geometry #Mathematics #Non-Euclidean geometry #Point processes and geometric inequalities #msc:51F15 #msc:51K05 #msc:52C25 #msc:68M10 #msc:68R10 #msc:70B15 #msc:90B18 #msc:90C26 #msc:91C15 #msc:92E10 #q-bio.QM

paper · pdf · open access · doi:10.1137/120875909

published in SIAM Review 56(1), 3-69 (Society for Industrial and Applied Mathematics) · 64 pages, 21 figures

arxiv created 2012/05/02 · arxiv updated 2012/05/03 · openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis on molecular conformation problems.

Citations

• Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization
• Some distance properties of latent root and vector methods used in multivariate analysis
• Untersuchungen �ber allgemeine Metrik

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