| Bibtype |
Inproceedings |
| Bibkey |
Sohler/Woodruff/2018a |
| Author |
Sohler, Christian and Woodruff, David P. |
| Editor |
Thorup, Mikkel |
| Title |
Strong Coresets for $k$-Median and Subspace Approximation: Goodbye Dimension |
| Booktitle |
59th {IEEE} Annual Symposium on Foundations of Computer Science, {FOCS} |
| Pages |
802--813 |
| Publisher |
{IEEE} Computer Society |
| Abstract |
We obtain the first strong coresets for the $k$-median and subspace approximation problems with sum of distances objective function, on $n$ points in $d$ dimensions, with a number of weighted points that is independent of both $n$ and $d$; namely, our coresets have size $poly(k/\eps)$. A strong coreset $(1 + \eps)$-approximates the cost function for all possible sets of centers simultaneously. We also give
efficient $nnz(A)+(n+d)poly(k/\eps)+exp(poly(k/\eps))$ time algorithms for computing these coresets.
We obtain the result by introducing a new dimensionality reduction technique for coresets that significantly generalizes an earlier result of Feldman, Sohler and Schmidt for squared Euclidean distances to sums of $p$-th powers of Euclidean distances for constant $p\geq 1$.
|
| Year |
2018 |
| Projekt |
SFB876-A2 |
