Generalized Center Problems with Outliers

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 ∈ 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 the...

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Bibliographic Details
Published inACM transactions on algorithms Vol. 15; no. 3; pp. 1 - 14
Main Authors Chakrabarty, Deeparnab, Negahbani, Maryam
Format Journal Article
LanguageEnglish
Published New York, NY, USA ACM 01.07.2019
Subjects
Approximation algorithms analysis
Design and analysis of algorithms
Facility location and clustering
Theory of computation
Approximation algorithms
k-center problem
clustering
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Summary: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 ∈ 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.
ISSN:1549-6325
1549-6333
DOI:10.1145/3338513