IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-5128-0_5.html
   My bibliography  Save this book chapter

Is the Distance Geometry Problem in NP?

In: Distance Geometry

Author

Listed:
  • Nathanael Beeker

    (CMAP, École Polytechnique)

  • Stéphane Gaubert

    (INRIA Rocquencourt)

  • Christian Glusa

    (CMAP, École Polytechnique)

  • Leo Liberti

    (LIX, École Polytechnique)

Abstract

Given a weighted undirected graph $$G = (V,E,d)$$ with $$d : E \rightarrow {\mathbb{Q}}_{+}$$ and a positive integer K, the distance geometry problem (DGP) asks to find an embedding $$x : V \rightarrow {\mathbb{R}}^{K}$$ of G such that for each edge $$\{i,j\}$$ we have $$\|{x}_{i} - {x}_{j}\| = {d}_{ij}$$ . Saxe proved in 1979 that the DGP is NP-complete with K = 1 and doubted the applicability of the Turing machine model to the case with K > 1, because the certificates for YES instances might involve real numbers. This chapter is an account of an unfortunately failed attempt to prove that the DGP is in NP for K = 2. We hope that our failure will motivate further work on the question.

Suggested Citation

  • Nathanael Beeker & Stéphane Gaubert & Christian Glusa & Leo Liberti, 2013. "Is the Distance Geometry Problem in NP?," Springer Books, in: Antonio Mucherino & Carlile Lavor & Leo Liberti & Nelson Maculan (ed.), Distance Geometry, edition 127, chapter 0, pages 85-93, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-5128-0_5
    DOI: 10.1007/978-1-4614-5128-0_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4614-5128-0_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.