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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [25 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02169579
Contributor : Vincent Cohen-Addad <>
Submitted on : Monday, July 1, 2019 - 12:29:52 PM
Last modification on : Wednesday, July 10, 2019 - 1:35:55 AM

File

main.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

41

Files downloads

48