Tight FPT Approximations for k-Median and k-Means

Vincent Cohen-Addad (1, 2) , Anupam Gupta (3) , Amit Kumar , Euiwoong Lee , Jason Li

1 CNRS - Centre National de la Recherche Scientifique
2 RO - Recherche Opérationnelle
3 Computer Science Department - Carnegie Mellon University

We investigate the fine-grained complexity of approximating the classical k-Median/k-Means clustering problems in general metric spaces. We show how to improve the approximation factors to (1 + 2/e + ε) and (1 + 8/e + ε) respectively, using algorithms that run in fixed-parameter time. Moreover, we show that we cannot do better in FPT time, modulo recent complexity-theoretic conjectures. 2012 ACM Subject Classification Theory of computation → Facility location and clustering; Theory of computation → Fixed parameter tractability; Theory of computation → Submodular optimization and polymatroids

Mots clés: k-median; fixed-parameter tractability; clustering; core-sets; and phrases approximation algorithms; k-means

Domaines: Algorithme et structure de données [cs.DS]

Vincent Cohen-Addad, Anupam Gupta, Amit Kumar, Euiwoong Lee, Jason Li. Tight FPT Approximations for k-Median and k-Means. 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019), Jul 2019, Patras, Greece. pp.42:1--42:14, ⟨10.4230/LIPIcs.ICALP.2019.42⟩. ⟨hal-02360773⟩