Abstract
In the k-median problem we are given a connected graph with non-negative weights associated with the nodes and lengths associated with the edges. The task is to compute locations of k facilities in order to minimize the sum of the weighted distances between each node and its closest facility. In this paper we consider the case when the graph is a tree. We show that this problem can be solved in time \(O(n {\mbox{\rm polylog}} (n))\) for the following cases: (i) directed trees (and any fixed k), (ii) balanced undirected trees, and (iii) undirected trees with k=3.
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Benkoczi, R., Bhattacharya, B., Chrobak, M., Larmore, L.L., Rytter, W. (2003). Faster Algorithms for k-Medians in Trees. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_16
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DOI: https://doi.org/10.1007/978-3-540-45138-9_16
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