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arXiv · 1805.02217

Generalized Center Problems with Outliers

Deeparnab Chakrabarty·Maryam Negahbani
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Abstract

We study the $\mathcal{F}$-center problem with outliers: given a metric space $(X,d)$, a general down-closed family $\mathcal{F}$ of subsets of $X$, and a parameter $m$, we need to locate a subset $S\in \mathcal{F}$ 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 $\mathcal{F}$-center problem with outliers if and only if we can efficiently optimize a poly-bounded linear function over $\mathcal{F}$ 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.

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Deeparnab Chakrabarty, Maryam Negahbani. 2018-05-06. Generalized Center Problems with Outliers. https://arxiv.org/abs/1805.02217

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