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This paper describes an O(nlogn) algorithm for finding the optimal location of a tree shaped facility of a specified size in a tree network with n nodes, using the centdian criterion: a convex combination of the weighted average distance and the maximum weighted distance from the facility to the demand points (nodes of the tree). These optimization criteria introduced by Halpern, combine the weighted...
The p-facility centdian network problem consists of finding the p points that minimize a convex combination of the p-center and p-median objective functions. The vertices and local centers constitute a dominating set for the 1-facility centdian; i.e., it contains an optimal solution for all instances of the problem. Hooker et al. (1991) give a theoretical result to extend the dominating sets for the...
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