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A Constant Approximation for Colorful k-Center

Authors Sayan Bandyapadhyay, Tanmay Inamdar, Shreyas Pai, Kasturi Varadarajan

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Author Details

Sayan Bandyapadhyay
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Tanmay Inamdar
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Shreyas Pai
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA
Kasturi Varadarajan
  • Department of Computer Science, University of Iowa, Iowa City, IA, USA

Funding

The first, second and fourth authors are partially supported by the National Science Foundation under Grant CCF-1615845.

Cite AsGet BibTex

Sayan Bandyapadhyay, Tanmay Inamdar, Shreyas Pai, and Kasturi Varadarajan. A Constant Approximation for Colorful k-Center. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ESA.2019.12

Abstract

In this paper, we consider the colorful k-center problem, which is a generalization of the well-known k-center problem. Here, we are given red and blue points in a metric space, and a coverage requirement for each color. The goal is to find the smallest radius rho, such that with k balls of radius rho, the desired number of points of each color can be covered. We obtain a constant approximation for this problem in the Euclidean plane. We obtain this result by combining a "pseudo-approximation" algorithm that works in any metric space, and an approximation algorithm that works for a special class of instances in the plane. The latter algorithm uses a novel connection to a certain matching problem in graphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Facility location and clustering
  • Theory of computation → Computational geometry
Keywords
  • Colorful k-center
  • Euclidean Plane
  • LP Rounding
  • Outliers

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References

  1. Suman K Bera, Shalmoli Gupta, Amit Kumar, and Sambuddha Roy. Approximation algorithms for the partition vertex cover problem. Theoretical Computer Science, 555:2-8, 2014. Google Scholar
  2. André Berger, Vincenzo Bonifaci, Fabrizio Grandoni, and Guido Schäfer. Budgeted matching and budgeted matroid intersection via the gasoline puzzle. Mathematical Programming, 128(1-2):355-372, 2011. Google Scholar
  3. Paolo M. Camerini, Giulia Galbiati, and Francesco Maffioli. Random pseudo-polynomial algorithms for exact matroid problems. Journal of Algorithms, 13(2):258-273, 1992. Google Scholar
  4. Deeparnab Chakrabarty, Prachi Goyal, and Ravishankar Krishnaswamy. The Non-Uniform k-Center Problem. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2016. Google Scholar
  5. Deeparnab Chakrabarty and Maryam Negahbani. Generalized Center Problems with Outliers. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018. Google Scholar
  6. 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, pages 642-651. Society for Industrial and Applied Mathematics, 2001. Google Scholar
  7. Danny Z Chen, Jian Li, Hongyu Liang, and Haitao Wang. Matroid and knapsack center problems. Algorithmica, 75(1):27-52, 2016. Google Scholar
  8. Ke Chen. A constant factor approximation algorithm for k-median clustering with outliers. In Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, pages 826-835. Citeseer, 2008. Google Scholar
  9. Tomás Feder and Daniel Greene. Optimal algorithms for approximate clustering. In Proceedings of the twentieth annual ACM symposium on Theory of computing, pages 434-444. ACM, 1988. Google Scholar
  10. Zachary Friggstad, Kamyar Khodamoradi, Mohsen Rezapour, and Mohammad R Salavatipour. Approximation schemes for clustering with outliers. ACM Transactions on Algorithms (TALG), 15(2):26, 2019. Google Scholar
  11. Teofilo F Gonzalez. Clustering to minimize the maximum intercluster distance. Theoretical Computer Science, 38:293-306, 1985. Google Scholar
  12. MohammadTaghi Hajiaghayi, Rohit Khandekar, and Guy Kortsarz. Budgeted red-blue median and its generalizations. In European Symposium on Algorithms, pages 314-325. Springer, 2010. Google Scholar
  13. 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). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  14. Dorit S Hochbaum and Wolfgang Maass. Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM (JACM), 32(1):130-136, 1985. Google Scholar
  15. Dorit S Hochbaum and David B Shmoys. A best possible heuristic for the k-center problem. Mathematics of operations research, 10(2):180-184, 1985. Google Scholar
  16. Wen-Lian Hsu and George L Nemhauser. Easy and hard bottleneck location problems. Discrete Applied Mathematics, 1(3):209-215, 1979. Google Scholar
  17. Tanmay Inamdar and Kasturi R. Varadarajan. On the Partition Set Cover Problem. CoRR, abs/1809.06506, 2018. URL: http://arxiv.org/abs/1809.06506.
  18. Kamal Jain, Mohammad Mahdian, Evangelos Markakis, Amin Saberi, and Vijay V Vazirani. Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. Journal of the ACM (JACM), 50(6):795-824, 2003. Google Scholar
  19. Ravishankar Krishnaswamy, Shi Li, and Sai Sandeep. Constant approximation for k-median and k-means with outliers via iterative rounding. In Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pages 646-659. ACM, 2018. Google Scholar
  20. Lap Chi Lau, Ramamoorthi Ravi, and Mohit Singh. Iterative methods in combinatorial optimization, volume 46. Cambridge University Press, 2011. Google Scholar
  21. Ketan Mulmuley, Umesh V Vazirani, and Vijay V Vazirani. Matching is as easy as matrix inversion. Combinatorica, 7(1):105-113, 1987. Google Scholar
  22. Christos H Papadimitriou and Mihalis Yannakakis. The complexity of restricted spanning tree problems. Journal of the ACM (JACM), 29(2):285-309, 1982. Google Scholar
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