Discrete Applied Mathematics
Algorithms for path medi-centers of a tree
Computers and Operations Research - location science
The Centdian subtree on tree networks
Discrete Applied Mathematics
The Level Ancestor Problem Simplified
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Improved algorithms for several network location problems with equality measures
Discrete Applied Mathematics
Locating tree-shaped facilities using the ordered median objective
Mathematical Programming: Series A and B
The path-variance problem on tree networks
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Extensive facility location problems on networks with equity measures
Discrete Applied Mathematics
The continuous and discrete path-variance problems on trees
Networks - Special Issue on Trees
Conditional location of path and tree shaped facilities on trees
Journal of Algorithms
Unreliable point facility location problems on networks
Discrete Applied Mathematics
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In this paper, we study the problem of locating path-shaped facilities on a tree network with non negative weights associated to the vertices and positive lengths associated to the edges. Our objective is to ensure low variability of the distribution of the distances from the demand points (clients) to a facility. In the location process, we take into account both the maximum and the minimum weighted distances of a client to a facility and we formulate our problem in order to minimize the ''Range'' function which is defined as the difference between the maximum and the minimum weighted distances from the vertices of the network to a facility. We discuss different formulations of the problem providing polynomial time algorithms for each of them. We solve in polynomial time all the above problems also when an additional constraint on the maximum length of the path is introduced.