Web: http://arxiv.org/abs/2206.11210

June 23, 2022, 1:11 a.m. | Mehrdad Ghadiri, Mohit Singh, Santosh S. Vempala

cs.LG updates on arXiv.org arxiv.org

We study approximation algorithms for the socially fair $(\ell_p,
k)$-clustering problem with $m$ groups, whose special cases include the
socially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems.
We present (1) a polynomial-time $(5+2\sqrt{6})^p$-approximation with at most
$k+m$ centers (2) a $(5+2\sqrt{6}+\epsilon)^p$-approximation with $k$ centers
in time $n^{2^{O(p)}\cdot m^2}$, and (3) a $(15+6\sqrt{6})^p$ approximation
with $k$ centers in time $k^{m}\cdot\text{poly}(n)$. The first result is
obtained via a refinement of the iterative rounding method using a sequence of
linear programs. …

algorithms approximation arxiv clustering

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