Annals of Operations Research

, Volume 271, Issue 1, pp 161–203 | Cite as

Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures

  • Simon J. L. Billinge
  • Phillip M. Duxbury
  • Douglas S. GonçalvesEmail author
  • Carlile Lavor
  • Antonio Mucherino
SI: 4OR Surveys


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.


Distance geometry Graph rigidity Molecular conformations Nanostructures 



The authors are thankful to the editors for their invitation to submit an updated version of our survey that was previously published in 2016 in the Quarterly Journal of Operations Research. We wish to thank FAPESP and CNPq for financial support. Support for work at Michigan State University by the MSU foundation is gratefully acknowledged. Collaborations with Pavol Juhas, Luke Granlund, Saurabh Gujarathi, Chris Farrow and Connor Glosser are much appreciated. PMD, CL and AM would like to thank Leo Liberti for interesting and motivating discussions. Work in the Billinge group was supported by the U.S. National Science Foundation through grant DMREF-1534910.


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Authors and Affiliations

  1. 1.Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA
  2. 2.X-Ray Scattering GroupBrookhaven National LaboratoryUptonUSA
  3. 3.Department of Physics and AstronomyMichigan State UniversityEast LansingUSA
  4. 4.Centro de Ciências Físicas e MatemáticasUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  5. 5.Department of Applied Mathematics (IMECC-UNICAMP)University of CampinasCampinasBrazil
  6. 6.Institut de Recherche en Informatique et Systèmes AléatoiresUniversité de Rennes 1RennesFrance

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