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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.10
A Lottery Model for Center-Type Problems with Outliers

Authors: David G. Harris, Thomas Pensyl, Aravind Srinivasan, and Khoa Trinh

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
In this paper, we give tight approximation algorithms for the k-center and matroid center problems with outliers. Unfairness arises naturally in this setting: certain clients could always be considered as outliers. To address this issue, we introduce a lottery model in which each client is allowed to submit a parameter indicating the lower-bound on the probability that it should be covered and we look for a random solution that satisfies all the given requests. Out techniques include a randomized rounding procedure to round a point inside a matroid intersection polytope to a basis plus at most one extra item such that all marginal probabilities are preserved and such that a certain linear function of the variables does not decrease in the process with probability one.
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David G. Harris, Thomas Pensyl, Aravind Srinivasan, and Khoa Trinh. A Lottery Model for Center-Type Problems with Outliers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{harris_et_al:LIPIcs.APPROX-RANDOM.2017.10,
  author =	{Harris, David G. and Pensyl, Thomas and Srinivasan, Aravind and Trinh, Khoa},
  title =	{{A Lottery Model for Center-Type Problems with Outliers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.10},
  URN =		{urn:nbn:de:0030-drops-75596},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.10},
  annote =	{Keywords: approximation algorithms, randomized rounding, clustering problems}
}
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