Geodesic
Weighted admissible absolute 1-center problem
Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2020), pp. 3-9.

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This paper presents a polynomial algorithm for new generalization of the absolute 1-center problem (A1CP) in general undirected graph with each edge having a positive weight vector (length for the first coordinate and costs for all the other coordinates) and with each vertex having non-negative weight vector. We assume that the cost is a linear function of the length on edge. Non-negative cost boundaries are also given. AA1CP (admissible absolute 1-center problem) minimizes the weighted length of path between a point on edge and the farthest vertex provided that any weighted cost of path from the point to any vertex does not exceed the corresponding cost boundary.
Keywords: vertex-weighted absolute 1-center problem, admissible absolute 1-center problem. 
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     author = {S. I. Fainshtein and A. S. Fainshtein and V. E. Torchinsky},
     title = {Weighted admissible absolute 1-center problem},
     journal = {Informacionnye tehnologii i vy\v{c}islitelnye sistemy},
     pages = {3--9},
     publisher = {mathdoc},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ITVS_2020_2_a0/}
}
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S. I. Fainshtein; A. S. Fainshtein; V. E. Torchinsky. Weighted admissible absolute 1-center problem. Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2020), pp. 3-9. http://geodesic.mathdoc.fr/item/ITVS_2020_2_a0/