Distance Geometry

Theory, Methods, and Applications

  • Antonio Mucherino
  • Carlile Lavor
  • Leo Liberti
  • Nelson Maculan

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Ioannis Z. Emiris, Elias P. Tsigaridas, Antonios Varvitsiotis
      Pages 23-45
    3. Leo Liberti, Carlile Lavor, Antonio Mucherino
      Pages 47-60
    4. Nathanael Beeker, Stéphane Gaubert, Christian Glusa, Leo Liberti
      Pages 85-93
    5. Pavel Chebotarev, Michel Deza
      Pages 121-135
  3. Methods

    1. Front Matter
      Pages 137-137
    2. Zachary Voller, Zhijun Wu
      Pages 139-159
    3. Pedro Nucci, Loana Tito Nogueira, Carlile Lavor
      Pages 161-176
    4. Marco Locatelli, Fabio Schoen
      Pages 197-212
    5. Hoai An Le Thi, Tao Pham Dinh
      Pages 225-290
  4. Applications to Protein Conformations

    1. Front Matter
      Pages 313-313
    2. Thérèse E. Malliavin, Antonio Mucherino, Michael Nilges
      Pages 329-350
  5. Back Matter
    Pages 413-420

About this book


Distance Geometry: Theory, Methods, and Applications is the first collection of research surveys dedicated to distance geometry and its applications. The first part of the book discusses theoretical aspects of the Distance Geometry Problem (DGP), where the relation between DGP and other related subjects are also presented. Covered topics include distance matrix theory, Euclidean distance matrix completion, multispherical structure of distance matrices, geometric algebra, algebraic distance geometry theory, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP.

The second part of this volume presents mathematical and computational properties of methods developed to the problems discussed in the first portion, including continuous methods (based on Gaussian and hyperbolic smoothing, difference of convex functions, semidefinite programming, branch-and-bound), discrete methods (based on branch-and-prune, geometric build-up, graph rigidity), and also heuristics methods (based on simulated annealing, genetic algorithms, tabu search, variable neighborhood search).

Applications comprise the third part of the book, which is mainly devoted to the application of DGP to NMR structure calculation. This is an important and strongly multidisciplinary application in biology and biomedicine.


Distance Geometry Graph Drawing Molecular Conformation Nuclear Magnetic Resonance Sensor Network Localization

Editors and affiliations

  • Antonio Mucherino
    • 1
  • Carlile Lavor
    • 2
  • Leo Liberti
    • 3
  • Nelson Maculan
    • 4
  1. 1.IRISA, University of Rennes 1RennesFrance
  2. 2., Dept of Applied Maths (IMECC-UNICAMP)State University of CampinasCampinasBrazil
  3. 3., LIXEcole PolytechniquePalaiseauFrance
  4. 4.Instituto Alberto Luiz Coimbra de, Pos-Graduacao e Pesquisa deUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

Bibliographic information