The cardinality constrained inverse center location problems on tree networks with edge length augmentation

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In a cardinality constrained inverse center location problem on networks, the goal is to modify the edge lengths at the minimum total cost subject to the given modification bounds so that a prespecified vertex becomes an absolute center location of the underlying network under the perturbed edge lengths and further the cardinality of the modified edge lengths obeys an upper bound. Using a set of self-constructed red-black search trees, as a suitable data structure, we propose novel optimal algorithms with polynomial time complexities for the problem on tree networks under various cost norms.