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Leo Liberti (leolibertigmail.com) Abstract: Distance geometry problems arise from the need to position entities in the Euclidean $K$space given some of their respective distances. Entities may be atoms (molecular distance geometry), wireless sensors (sensor network localization), or abstract vertices of a graph(graph drawing). In the context of molecular distance geometry, the distances are usually known because of chemical properties and Nuclear Magnetic Resonance experiments; sensor networks can estimate their relative distance by recording the power loss during a twoway exchange; finally, when drawing graphs in 2D or 3D, the graph to be drawn is given, and therefore distances between vertices can be computed. Distance geometry problems involve a search in continuous Euclidean space, but sometimes the problem structure helps reduce the search to a discrete set of points. In this paper we survey both continuous and discrete methods for solving some problems of molecular distance geometry. Keywords: distance geometry, rigidity, network localization, branchandprune Category 1: Applications  Science and Engineering (Biomedical Applications ) Category 2: Combinatorial Optimization (Other ) Citation: Download: [PDF] Entry Submitted: 09/27/2009 Modify/Update this entry  
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