Abstract
Let a connected undirected graph G = (V, E) be given. In the classical p-median problem we want to find a set X containing p points in G such that the sum of weighted distances from X to all vertices in V is minimized. We consider the semi-obnoxious case where every vertex has either a positive or negative weight. In this case we have two different objective functions: the sum of the minimum weighted distances from X to all vertices and the sum of the weighted minimum distances. In this paper we show that for the case p = 3 an optimal solution for the second model in a tree can be found in O(n 5) time. If the 3-median is restricted to vertices or if the tree is a path then the complexity can be reduced to O(n 3).
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This research has partially been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung.
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Burkard, R.E., Fathali, J. A polynomial method for the pos/neg weighted 3-median problem on a tree. Math Meth Oper Res 65, 229–238 (2007). https://doi.org/10.1007/s00186-006-0121-1
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DOI: https://doi.org/10.1007/s00186-006-0121-1