2-medians in trees with pos/neg weights
Discrete Applied Mathematics
An Approach to Location Models Involving Sets as Existing Facilities
Mathematics of Operations Research
Cardinality constrained facility location problems in trees
Cardinality constrained facility location problems in trees
Center location problems on tree graphs with subtree-shaped customers
Discrete Applied Mathematics
A new template for solving p-median problems for trees in sub-quadratic time
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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In this paper we consider the pos/neg-weighted median problem on a tree graph where the customers are modeled as continua subtrees. We address the discrete and continuous models, i.e., the subtrees' boundary points are all vertices, or possibly inner points of an edge, respectively. We consider two different objective functions. If we minimize the overall sum of the minimum weighted distances of the subtrees from the facilities, there exists an optimal solution satisfying a generalized vertex optimality property, e.g., there is an optimal solution such that all facilities are located at vertices or the boundary points of the subtrees. Based on this property we devise a polynomial time algorithm for the pos/neg-weighted 1-median problem on a tree with subtree-shaped customers.