Faster Algorithms for k-Medians in Trees

  • Robert Benkoczi
  • Binay Bhattacharya
  • Marek Chrobak
  • Lawrence L. Larmore
  • Wojciech Rytter
Conference paper

DOI: 10.1007/978-3-540-45138-9_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Robert Benkoczi
    • 1
  • Binay Bhattacharya
    • 1
  • Marek Chrobak
    • 2
  • Lawrence L. Larmore
    • 3
  • Wojciech Rytter
    • 4
    • 5
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Computer ScienceUniversity of CaliforniaRiversideUSA
  3. 3.Department of Computer ScienceUniversity of NevadaLas VegasUSA
  4. 4.Instytut InformatykiUniwersytet WarszawskiWarszawaPoland
  5. 5.Department of Computer Science, and New Jersey Institute of TechnologyNewarkUSA

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