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In the 2 years since our last 4OR review of distance geometry methods with applications to proteins and nanostructures, there has been rapid progress in treating uncertainties in the discretizable distance geometry problem; and a new class of geometry problems started to be explored, namely vector geometry problems. In this work we review this progress in the context of the earlier literature.
Considering geometry based on the concept of distance, the results found by Menger and Blumenthal originated a body of knowledge called distance geometry. This survey covers some recent developments for assigned and unassigned distance geometry and focuses on two main applications: determination of three-dimensional conformations of biological molecules and nanostructures.
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