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Generalized $k$-Center Problems

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44477

Garg,  Naveen
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44233

Chaudhuri,  Shiva
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Fulltext (public)

1996-1-021
(Any fulltext), 10KB

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Citation

Garg, N., Chaudhuri, S., & Ravi, R.(1996). Generalized $k$-Center Problems (MPI-I-1996-1-021). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A121-4
Abstract
The $k$-center problem with triangle inequality is that of placing $k$ center nodes in a weighted undirected graph in which the edge weights obey the triangle inequality, so that the maximum distance of any node to its nearest center is minimized. In this paper, we consider a generalization of this problem where, given a number $p$, we wish to place $k$ centers so as to minimize the maximum distance of any node to its $p\th$ closest center. We consider three different versions of this reliable $k$-center problem depending on which of the nodes can serve as centers and non-centers and derive best possible approximation algorithms for all three versions.