Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentially Private Clustering: Tight Approximation Ratios   We study the task of differentially private clustering. For several basic
clustering problems, including Euclidean DensestBall, 1-Cluster, k-means, and
k-median, we give efficient differentially private algorithms that achieve
essentially the same approximation ratios as those that can be obtained by any
non-private algorithm, while incurring only small additive errors. This
improves upon existing efficient algorithms that only achieve some large
constant approximation factors.
  Our results also imply an improved algorithm for the Sample and Aggregate
privacy framework. Furthermore, we show that one of the tools used in our
1-Cluster algorithm can be employed to get a faster quantum algorithm for
ClosestPair in a moderate number of dimensions.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con