Clustering What Matters: Optimal Approximation for Clustering with Outliers

Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set X n points and two numbers k m, clustering aims to exclude m from X, partition remaining into clusters that minimizes certain cost function. In this paper, we give general approach for solving outliers, which results fixed-parameter tractable (FPT) algorithm (i.e., an running time form f(k, m) * poly(n) some function f), almost matches approximation ratio its outlier-free counterpart. As corollary, obtain FPT algorithms optimal ratios k-Median k-Means Euclidean metrics. We also exhibit more applications our other variants problem impose additional constraints on clustering, such as fairness or matroid constraints.