2026-07-20T11:02:41Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9033 2024-03-06T10:43:12Z ddc:004 open_access

Interpolating between k-Median and k-Center: Approximation Algorithms for Ordered k-Median Chakrabarty, Deeparnab Swamy, Chaitanya Approximation algorithms Clustering Facility location Primal-dual method We consider a generalization of k-median and k-center, called the ordered k-median problem. In this problem, we are given a metric space (D,{c_{ij}}) with n=|D| points, and a non-increasing weight vector w in R_+^n, and the goal is to open k centers and assign each point j in D to a center so as to minimize w_1 *(largest assignment cost)+w_2 *(second-largest assignment cost)+...+w_n *(n-th largest assignment cost). We give an (18+epsilon)-approximation algorithm for this problem. Our algorithms utilize Lagrangian relaxation and the primal-dual schema, combined with an enumeration procedure of Aouad and Segev. For the special case of {0,1}-weights, which models the problem of minimizing the l largest assignment costs that is interesting in and of by itself, we provide a novel reduction to the (standard) k-median problem, showing that LP-relative guarantees for k-median translate to guarantees for the ordered k-median problem; this yields a nice and clean (8.5+epsilon)-approximation algorithm for {0,1} weights. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Deeparnab Chakrabarty and Chaitanya Swamy 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.29 urn:nbn:de:0030-drops-90335 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.29 eng https://creativecommons.org/licenses/by/3.0/legalcode