A Lottery Model for Center-Type Problems with Outliers

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

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David G. Harris
Thomas Pensyl
Aravind Srinivasan
Khoa Trinh

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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)


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.
  • approximation algorithms
  • randomized rounding
  • clustering problems


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  1. Deeparnab Chakrabarty, Prachi Goyal, and Ravishankar Krishnaswamy. The non-uniform k-center problem. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), volume 55, pages 67:1-67:15, 2016. Google Scholar
  2. Moses Charikar, Samir Khuller, David M. Mount, and Giri Narasimhan. Algorithms for facility location problems with outliers. In Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA'01, pages 642-651, Philadelphia, PA, USA, 2001. Society for Industrial and Applied Mathematics. URL: http://dl.acm.org/citation.cfm?id=365411.365555.
  3. Danny Z. Chen, Jian Li, Hongyu Liang, and Haitao Wang. Matroid and knapsack center problems. Integer Programming and Combinatorial Optimization: 16th International Conference, IPCO 2013, Valparaíso, Chile, March 18-20, 2013. Proceedings, pages 110-122, 2013. URL: http://dx.doi.org/10.1007/978-3-642-36694-9_10.
  4. David Harris, Thomas Pensyl, Aravind Srinivasan, and Khoa Trinh. Fairness in resource allocation and slowed-down dependent rounding. Manuscript, 2017. Google Scholar
  5. Dorit S. Hochbaum and David B. Shmoys. A unified approach to approximation algorithms for bottleneck problems. J. ACM, 33(3):533-550, May 1986. URL: http://dx.doi.org/10.1145/5925.5933.
  6. Wen-Lian Hsu and George L. Nemhauser. Easy and hard bottleneck location problems. Discrete Applied Mathematics, 1(3):209-215, 1979. URL: http://dx.doi.org/10.1016/0166-218X(79)90044-1.
  7. Ravishankar Krishnaswamy, Amit Kumar, Viswanath Nagarajan, Yogish Sabharwal, and Barna Saha. The matroid median problem. In Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1117-1130. SIAM, 2011. Google Scholar
  8. Lap-Chi Lau, R. Ravi, and Mohit Singh. Iterative Methods in Combinatorial Optimization. Cambridge University Press, New York, NY, USA, 1st edition, 2011. Google Scholar
  9. Alexander Schrijver. Combinatorial optimization: polyhedra and efficiency, volume 24. Springer Science &Business Media, 2003. Google Scholar
  10. Chaitanya Swamy. Improved approximation algorithms for matroid and knapsack median problems and applications. In APPROX/RANDOM 2014, volume 28, pages 403-418, 2014. Google Scholar
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