The unassigned distance geometry problem

Duxbury, P. M.; Granlund, L.; Gujarathi, S. R.; Juhas, P.; Billinge, S. J. L.

doi:10.1016/j.dam.2015.10.029

Title: The unassigned distance geometry problem

Abstract

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.

Authors:: Duxbury, P. M.; Granlund, L.; Gujarathi, S. R.; Juhas, P.; Billinge, S. J. L.

Publication Date:: Sun May 01 00:00:00 EDT 2016

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1252533

Alternate Identifier(s):: OSTI ID: 1336154

Report Number(s):: BNL-112665-2016-JA
Journal ID: ISSN 0166-218X; S0166218X15005168; PII: S0166218X15005168

Grant/Contract Number:: AC02-98CH10886; SC00112704

Resource Type:: Published Article

Journal Name:: Discrete Applied Mathematics

Additional Journal Information:: Journal Name: Discrete Applied Mathematics Journal Volume: 204 Journal Issue: C; Journal ID: ISSN 0166-218X

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Nanostructure; Rigid cluster; Percolation; Unassigned distances; LIGA; TRIBOND

Citation Formats


                    Duxbury, P. M., Granlund, L., Gujarathi, S. R., Juhas, P., and Billinge, S. J. L. The unassigned distance geometry problem.  Netherlands: N. p., 2016. 
Web.  doi:10.1016/j.dam.2015.10.029.

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                    Duxbury, P. M., Granlund, L., Gujarathi, S. R., Juhas, P., & Billinge, S. J. L. The unassigned distance geometry problem.  Netherlands.  https://doi.org/10.1016/j.dam.2015.10.029

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                    Duxbury, P. M., Granlund, L., Gujarathi, S. R., Juhas, P., and Billinge, S. J. L. Sun .  
"The unassigned distance geometry problem".  Netherlands.  https://doi.org/10.1016/j.dam.2015.10.029.

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@article{osti_1252533,

  title        = {The unassigned distance geometry problem},

  author       = {Duxbury, P. M. and Granlund, L. and Gujarathi, S. R. and Juhas, P. and Billinge, S. J. L.},

  abstractNote = {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.},

  doi          = {10.1016/j.dam.2015.10.029},

  journal      = {Discrete Applied Mathematics},

  number       = C,

  volume       = 204,

  place        = {Netherlands},

  year         = {Sun May 01 00:00:00 EDT 2016},

  month        = {Sun May 01 00:00:00 EDT 2016}

}

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