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Balanced location on a graph. (English) Zbl 0874.90114
Summary: The problem of locating service facilities with respect to a given set of demands on a graph is considered. The objective function to be minimized is equal to the maximum difference in the distance from a demand point to its farthest and nearest facility (balancing function). It is assumed that any facility has at most \(m\) possibilities for its location. For \(m=2\), the computational complexity of the problem is \(O(np^2\log p)\), where \(n\) is the number of demand points and \(p\) is the number of located facilities. For \(m>2\), the problem is NP-hard. Similar results are presented for boolean and strongly boolean versions of the problem.

MSC:
90B80 Discrete location and assignment
90C35 Programming involving graphs or networks
90C60 Abstract computational complexity for mathematical programming problems
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