On clustering with discounts

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 contrib...

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Bibliographic Details
Published in:Information processing letters Vol. 177; p. 106272
Main Author: Deng, Shichuan
Format: Journal Article
Language:English
Published: Elsevier B.V 01.08.2022
Subjects:
Approximation algorithms
Clustering with discounts
Knapsack constraint
Matroid constraint
Approximation algorithms
Matroid constraint
Clustering with discounts
Knapsack constraint
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary: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.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2022.106272