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Distance Geometry in Linearizable Norms

  • Claudia D’Ambrosio
  • Leo Liberti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10589)

Abstract

Distance Geometry puts the concept of distance at its center. The basic problem in distance geometry could be described as drawing an edge-weighted undirected graph in \(\mathbb {R}^K\) for some given K such that the positions for adjacent vertices have distance which is equal to the corresponding edge weight. There appears to be a lack of exact methods in this field using any other norm but \(\ell _2\). In this paper we move some first steps using the \(\ell _1\) and \(\ell _\infty \) norms: we discuss worst-case complexity, propose mixed-integer linear programming formulations, and sketch a few heuristic ideas.

Keywords

Distance geometry Norms Mathematical programming 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LIX CNRS (UMR7161)École PolytechniquePalaiseauFrance

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