Random projections for the distance geometry problem

• Leo Liberti ; Benedetto Manca ^[1] ; Pierre-Louis Poirion ^[2]
  1. [1] University of Cagliari

     University of Cagliari

     Cagliari, Italia

     
  2. [2] RIKEN Center for Advanced Intelligence Project, Tokyo
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 181-187
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Random projections decrease the dimensionality of a finite set of vectors while ensuringapproximate congruence, up to a multiplicative constant. Based on the theory of randomprojections in conic programming we derive an application of random projections to anonconvex mathematical programming problem in distance geometry, namely that of findingthe positions of the vertices of a graph in a vector space of given dimension, while ensuring thatevery pair of adjacent vertices is placed at a Euclidean distance equal to the correspondingedge weight.