Reverse 1-maxian problem with keeping existing 1-median
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Here we investigate the reverse 1-maxian problem when it is necessary to keep 1-median of a given network. This problem asks to modify the parameters of the network so that the 1-median does not change and the candidate place for 1-maxian improves as much as possible. For the uniform-cost model on a tree graph, an algorithm with \(O(n \log n)\) time complexity is developed. It is also shown that the problem is solvable in linear time where it is only allowed to increase the vertex weights.
KeywordsFacility location 1-maxian problem Reverse optimization Obnoxious location problem
Mathematics Subject Classification90C35 90C27 90C05
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