eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
30:1
30:14
10.4230/LIPIcs.ICALP.2018.30
article
Generalized Center Problems with Outliers
Chakrabarty, Deeparnab
1
Negahbani, Maryam
2
Department of Computer Science, Dartmouth College, 9 Maynard St, Hanover, NH, USA , https://web.cs.dartmouth.edu/people/deeparnab-chakrabarty
Department of Computer Science, Dartmouth College, 9 Maynard St, Hanover, NH, USA
We study the F-center problem with outliers: given a metric space (X,d), a general down-closed family F of subsets of X, and a parameter m, we need to locate a subset S in F of centers such that the maximum distance among the closest m points in X to S is minimized.
Our main result is a dichotomy theorem. Colloquially, we prove that there is an efficient 3-approximation for the F-center problem with outliers if and only if we can efficiently optimize a poly-bounded linear function over F subject to a partition constraint. One concrete upshot of our result is a polynomial time 3-approximation for the knapsack center problem with outliers for which no (true) approximation algorithm was known.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.30/LIPIcs.ICALP.2018.30.pdf
Approximation Algorithms
Clustering
k-Center Problem