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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.

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