%AMakarychev, Konstantin%AShan, Liren%D2023%INeurIPS 2023
%K
%MOSTI ID: 10519127
%PMedium: X
%TRandom Cuts are Optimal for Explainable k-Medians
%XWe show that the RandomCoordinateCut algorithm gives the optimal competitive ratio for explainable k-medians in l1. The problem of explainable k-medians was introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian in 2020. Several groups of authors independently proposed a simple polynomial-time randomized algorithm for the problem and showed that this algorithm is O(log k loglog k) competitive. We provide a tight analysis of the algorithm and prove that its competitive ratio is upper bounded by 2ln k +2. This bound matches the Omega(log k) lower bound by Dasgupta et al (2020).
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