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Open Research Areas in Distance Geometry

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Open Problems in Optimization and Data Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 141))

Abstract

Distance geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open and promising research areas.

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Notes

  1. 1.

    Direct problems may not be all that easy: see Erdős’ unit distances and distinct distances problems [63].

  2. 2.

    Another, and possibly better, candidate is the Graph Isomorphism problem [12, 13].

  3. 3.

    See, e.g., https:en.wikipedia.org/wiki/Classification_of_manifolds.

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Acknowledgements

We are grateful for Ana Flavia Lima for helping to check the manuscript prior to submission. LL was partly supported by the ANR “Bip:Bip” project n. ANR-10-BINF-03-08. CL was partly supported by the Brazilian research agencies FAPESP, CNPq.

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Authors and Affiliations

  1. CNRS LIX, Ecole Polytechnique, Palaiseau, France

    Leo Liberti

  2. Department of Applied Mathematics (IMECC-UNICAMP), University of Campinas, Campinas, SP, Brazil

    Carlile Lavor

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  1. Leo Liberti
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  2. Carlile Lavor
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Correspondence to Leo Liberti .

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  1. Industrial and Systems, Engineering Department, University of Florida, Center For Applied Optimization, Gainesville, FL, USA

    Panos M. Pardalos

  2. Industrial Logistics, ETS Institute, Lulea University of Technology, Norrbotten, Sweden

    Athanasios Migdalas

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Liberti, L., Lavor, C. (2018). Open Research Areas in Distance Geometry. In: Pardalos, P., Migdalas, A. (eds) Open Problems in Optimization and Data Analysis. Springer Optimization and Its Applications, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-319-99142-9_11

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