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Title: The unassigned distance geometry problem

Studies of distance geometry problems (DGP) have focused on cases where the vertices at the ends of all or most of the given distances are known or assigned, which we call assigned distance geometry problems (aDGPs). In this contribution we consider the unassigned distance geometry problem (uDGP) where the vertices associated with a given distance are unknown, so the graph structure has to be discovered. uDGPs arises when attempting to find the atomic structure of molecules and nanoparticles using X-ray or neutron diffraction data from non-crystalline materials. Rigidity theory provides a useful foundation for both aDGPs and uDGPs, though it is restricted to generic realizations of graphs, and key results are summarized. Conditions for unique realization are discussed for aDGP and uDGP cases, build-up algorithms for both cases are described and experimental results for uDGP are presented.
 [1] ;  [1] ;  [1] ;  [2] ;  [3]
  1. Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy
  2. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
  3. Columbia Univ., New York, NY (United States). Dept. of Applied Physics and Applied Mathematics
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0166-218X; R&D Project: PO011; KC0201060
Grant/Contract Number:
SC00112704; AC02-98CH10886
Published Article
Journal Name:
Discrete Applied Mathematics
Additional Journal Information:
Journal Volume: 204; Journal Issue: C; Journal ID: ISSN 0166-218X
Research Org:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Nanostructure; Rigid cluster; Percolation; Unassigned distances; LIGA; TRIBOND