On the Fixed-Parameter Tractability of Capacitated Clustering - Archive ouverte HAL Access content directly
Conference Papers Year : 2019

On the Fixed-Parameter Tractability of Capacitated Clustering

Abstract

We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean space and general metric space is Theta(log k) and it remains a major open problem whether a constant factor exists. We show that there exists a (3+epsilon)-approximation algorithm for the capacitated k-median and a (9+epsilon)-approximation algorithm for the capacitated k-means problem in general metric spaces whose running times are f(epsilon,k) n^{O(1)}. For Euclidean inputs of arbitrary dimension, we give a (1+epsilon)-approximation algorithm for both problems with a similar running time. This is a significant improvement over the (7+epsilon)-approximation of Adamczyk et al. for k-median in general metric spaces and the (69+epsilon)-approximation of Xu et al. for Euclidean k-means.
Fichier principal
Vignette du fichier
main.pdf (547.82 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02169579 , version 1 (01-07-2019)

Identifiers

Cite

Vincent Cohen-Addad, Jason Li. On the Fixed-Parameter Tractability of Capacitated Clustering. 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), Jul 2019, Patras, Greece. pp.41:1--41:14, ⟨10.4230/LIPIcs.ICALP.2019.41⟩. ⟨hal-02169579⟩
152 View
406 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More