We consider the problem of finding an optimal location of a path on a tree:
using combinations of minisum and minimax criteria (which are respectively
maximal distance and average distance from the path to customers situated
at the vertices), The case of linear combination of the two criteria and th
e case where one criterion is optimized subject to a restriction on the val
ue of the other are considered and linear-time algorithms for these problem
s are presented. It is proved that the representation of the set of Pareto-
optimal paths in the space of criteria has cardinality not greater than n -
1, where n is the number of vertices of the tree, and can be obtained in O
(n log n ) time, although the number of Pareto-optimal paths can be O(n(2))
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