Random Cuts are Optimal for Explainable k-Medians
Data Structures and Algorithms
2023-04-19 v1
Abstract
We 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).
Keywords
Cite
@article{arxiv.2304.09113,
title = {Random Cuts are Optimal for Explainable k-Medians},
author = {Konstantin Makarychev and Liren Shan},
journal= {arXiv preprint arXiv:2304.09113},
year = {2023}
}
Comments
14 pages, 2 figures