Corpus ID: 67856665

Parameterized k-Clustering: The distance matters!

@article{Fomin2019ParameterizedKT,
  title={Parameterized k-Clustering: The distance matters!},
  author={Fedor V. Fomin and Petr A. Golovach and Kirill Simonov},
  journal={ArXiv},
  year={2019},
  volume={abs/1902.08559}
}
  • Fedor V. Fomin, Petr A. Golovach, Kirill Simonov
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • We consider the $k$-Clustering problem, which is for a given multiset of $n$ vectors $X\subset \mathbb{Z}^d$ and a nonnegative number $D$, to decide whether $X$ can be partitioned into $k$ clusters $C_1, \dots, C_k$ such that the cost \[\sum_{i=1}^k \min_{c_i\in \mathbb{R}^d}\sum_{x \in C_i} \|x-c_i\|_p^p \leq D,\] where $\|\cdot\|_p$ is the Minkowski ($L_p$) norm of order $p$. For $p=1$, $k$-Clustering is the well-known $k$-Median. For $p=2$, the case of the Euclidean distance, $k$-Clustering… CONTINUE READING
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