In the aversion k-clustering problem, given a metric space, we want to cluster the points into k clusters. The cost incurred by each point is the distance to the furthest point in its cluster, and the cost of the clustering is the sum of all these per-point-costs. This problem is motivated by questions in generating automatic abstractions of extensive-form games. We reduce this problem to a "local" k-median problem where each facility has a prescribed radius and can only connect to clients within that radius. Our main results is a constant-factor approximation algorithm for the aversion k-clustering problem via the local k-median problem. We use a primal-dual approach; our technical contribution is a non-local rounding step which we feel is of broader interest.
@InProceedings{gupta_et_al:LIPIcs.ICALP.2016.66, author = {Gupta, Anupam and Guruganesh, Guru and Schmidt, Melanie}, title = {{Approximation Algorithms for Aversion k-Clustering via Local k-Median}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {66:1--66:13}, 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.2016.66}, URN = {urn:nbn:de:0030-drops-62180}, doi = {10.4230/LIPIcs.ICALP.2016.66}, annote = {Keywords: Approximation algorithms, clustering, k-median, primal-dual} }
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