Dual Linear Programming Problem and OneDimensional Gromov Minimal Fillings of Finite Metric Spaces
Abstract
The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multitours appearing in the formula of weight of minimal fillings is improved, an alternative proof of this formula is obtained, and also explicit formulas for finite spaces consisting of $5$ and $6$ points are derived.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.10216
 Bibcode:
 2019arXiv190410216I
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Optimization and Control;
 51F99;
 90C35;
 90C08;
 49Q10;
 90C27
 EPrint:
 19 pages, 4 figures