Geometry and Analytics of the Multifacility Weber Problem

12/30/2019

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by   Alexei Yu. Uteshev, et al.

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For the Weber problem of construction of the minimal cost planar weighted network connecting four terminals with two extra facilities, the solution by radicals is proposed. The conditions for the existence of the network in the assumed topology and the explicit formulae for coordinates of the facilities are presented. The obtained results are utilized for investigation of the network dynamics under variation of parameters. Extension of the results to the general Weber problem is also discussed.