License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.10
URN: urn:nbn:de:0030-drops-75596
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7559/
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Harris, David G. ; Pensyl, Thomas ; Srinivasan, Aravind ; Trinh, Khoa

A Lottery Model for Center-Type Problems with Outliers

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LIPIcs-APPROX-RANDOM-2017-10.pdf (0.9 MB)

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.

BibTeX - Entry

@InProceedings{harris_et_al:LIPIcs:2017:7559,
  author =	{David G. Harris and Thomas Pensyl and Aravind Srinivasan and Khoa Trinh},
  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 =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7559},
  URN =		{urn:nbn:de:0030-drops-75596},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.10},
  annote =	{Keywords: approximation algorithms, randomized rounding, clustering problems}
}

Keywords: approximation algorithms, randomized rounding, clustering problems
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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