Dual Linear Programming Problem and One-Dimensional Gromov Minimal Fillings of Finite Metric Spaces
classification
🧮 math.MG
math.OC
keywords
fillingsfiniteminimalspacesformulalinearmetricproblem
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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 multi-tours 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.
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