We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural LP relaxation for the problem, one can only hope to get the violation factor down to 2. Li [SODA'16] introduced a novel LP to go beyond the limit of 2 and gave a constant-factor approximation algorithm that opens (1 + epsilon)*k facilities. We use the configuration LP of Li [SODA'16] to give a constant-factor approximation for the Capacitated k-Median problem in a seemingly harder configuration: we violate only the capacities by 1 + epsilon. This result settles the problem as far as pseudo-approximation algorithms are concerned.
@InProceedings{demirci_et_al:LIPIcs.ICALP.2016.73, author = {Demirci, G\"{o}kalp and Li, Shi}, title = {{Constant Approximation for Capacitated k-Median with (1+epsilon)-Capacity Violation}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {73:1--73:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.73}, URN = {urn:nbn:de:0030-drops-62112}, doi = {10.4230/LIPIcs.ICALP.2016.73}, annote = {Keywords: Approximation Algorithms, Capacitated k-Median, Pseudo Approximation, Capacity Violation} }
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