The k-center problem is a classic facility location problem, where given an
edge-weighted graph G=(V,E) one is to find a subset of k vertices S,
such that each vertex in V is "close" to some vertex in S. The
approximation status of this basic problem is well understood, as a simple
2-approximation algorithm is known to be tight. Consequently different
extensions were studied.
In the capacitated version of the problem each vertex is assigned a capacity,
which is a strict upper bound on the number of clients a facility can serve,
when located at this vertex. A constant factor approximation for the
capacitated k-center was obtained last year by Cygan, Hajiaghayi and Khuller
[FOCS'12], which was recently improved to a 9-approximation by An, Bhaskara and
Svensson [arXiv'13].
In a different generalization of the problem some clients (denoted as
outliers) may be disregarded. Here we are additionally given an integer p and
the goal is to serve exactly p clients, which the algorithm is free to
choose. In 2001 Charikar et al. [SODA'01] presented a 3-approximation for the
k-center problem with outliers.
In this paper we consider a common generalization of the two extensions
previously studied separately, i.e. we work with the capacitated k-center
with outliers. We present the first constant factor approximation algorithm
with approximation ratio of 25 even for the case of non-uniform hard
capacities.Comment: 15 pages, 3 figures, accepted to STACS 201