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Optimization Letters

, Volume 6, Issue 4, pp 783–796 | Cite as

Discretization orders for distance geometry problems

  • Carlile Lavor
  • Jon Lee
  • Audrey Lee-St. John
  • Leo Liberti
  • Antonio Mucherino
  • Maxim Sviridenko
Original Paper

Abstract

Given a weighted, undirected simple graph G = (V, E, d) (where \({d:E\to\mathbb{R}_+}\)), the distance geometry problem (DGP) is to determine an embedding \({x:V\to\mathbb{R}^K}\) such that \({\forall \{i,j\} \in E\;\|x_i-x_j\|=d_{ij}}\) . Although, in general, the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V. We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed dimension K. We present results of computational experiments on a set of protein backbones whose natural atomic order does not satisfy the order requirements and compare our approach with some available continuous space searches.

Keywords

Molecular distance geometry Proteins Sensor network localization Graph drawing 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Carlile Lavor
    • 1
  • Jon Lee
    • 2
  • Audrey Lee-St. John
    • 3
  • Leo Liberti
    • 4
  • Antonio Mucherino
    • 5
  • Maxim Sviridenko
    • 2
  1. 1.Department of Applied Mathematics (IMECC-UNICAMP)State University of CampinasCampinasBrazil
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA
  3. 3.Computer Science DepartmentMount Holyoke CollegeSouth HadleyUSA
  4. 4.LIX, École PolytechniquePalaiseauFrance
  5. 5.CERFACSToulouseFrance

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