On Clustering with Discounts
Abstract
We study the -median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most facilities. The goal is to minimize the sum of distances from each client to its nearest open facility which is discounted by its own discount value, with minimum contribution being zero. -median with discounts unifies many classic clustering problems, e.g., -center, -median, -facility -centrum, etc. We obtain a bi-criteria constant-factor approximation using an iterative LP rounding algorithm. Our result improves the previously best approximation guarantee for -median with discounts [Ganesh et al., ICALP'21]. We also devise bi-criteria constant-factor approximation algorithms for the matroid and knapsack versions of median clustering with discounts.
Keywords
Cite
@article{arxiv.2111.09505,
title = {On Clustering with Discounts},
author = {Shichuan Deng},
journal= {arXiv preprint arXiv:2111.09505},
year = {2021}
}