On clustering with discounts - Deng, Shichuan (Information processing letters, 2022)
We study the k-median with discounts problem, wherein we are given clients with non-negative discounts and seek to open at most k 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. We obtain a bi-criteria constant-factor approximation using an iterative LP rounding algorithm. Our result improves the previously best approximation guarantee for k-median with discounts (Ganesh et al. (2001) [9]). We also devise bi-criteria constant-factor approximation algorithms for the matroid and knapsack versions of median clustering with discounts. •Investigate clustering problems with discounts subject to general constraints.•Devise constant approximation algorithms using a unified iterative LP rounding method.•Modestly improve previously-known approximation guarantee for k-median with discounts.