LIPIcs.ICALP.2021.77.pdf
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Structural Iterative Rounding for Generalized k-Median Problems
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48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Colloquium on Automata, Languages, and Programming (ICALP) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2021-07-02
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Anupam Gupta, Benjamin Moseley, and Rudy Zhou. Structural Iterative Rounding for Generalized k-Median Problems. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 77:1-77:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ICALP.2021.77
Abstract
This paper considers approximation algorithms for generalized k-median problems. This class of problems can be informally described as k-median with a constant number of extra constraints, and includes k-median with outliers, and knapsack median. Our first contribution is a pseudo-approximation algorithm for generalized k-median that outputs a 6.387-approximate solution with a constant number of fractional variables. The algorithm is based on iteratively rounding linear programs, and the main technical innovation comes from understanding the rich structure of the resulting extreme points. Using our pseudo-approximation algorithm, we give improved approximation algorithms for k-median with outliers and knapsack median. This involves combining our pseudo-approximation with pre- and post-processing steps to round a constant number of fractional variables at a small increase in cost. Our algorithms achieve approximation ratios 6.994 + ε and 6.387 + ε for k-median with outliers and knapsack median, respectively. These both improve on the best known approximations.
Subject Classification
ACM Subject Classification
- Theory of computation → Facility location and clustering
Keywords
- approximation algorithms
- clustering
- linear programming
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References
- Vijay Arya, Naveen Garg, Rohit Khandekar, Adam Meyerson, Kamesh Munagala, and Vinayaka Pandit. Local search heuristics for k-median and facility location problems. SIAM J. Comput., 33(3):544-562, 2004. URL: https://doi.org/10.1137/S0097539702416402.
- Jaroslaw Byrka, Thomas W. Pensyl, Bartosz Rybicki, Joachim Spoerhase, Aravind Srinivasan, and Khoa Trinh. An improved approximation algorithm for knapsack median using sparsification. Algorithmica, 80(4):1093-1114, 2018. URL: https://doi.org/10.1007/s00453-017-0294-4.
- Jaroslaw Byrka, Thomas W. Pensyl, Bartosz Rybicki, Aravind Srinivasan, and Khoa Trinh. An improved approximation for k-median and positive correlation in budgeted optimization. ACM Trans. Algorithms, 13(2):23:1-23:31, 2017. URL: https://doi.org/10.1145/2981561.
-
Moses Charikar, Samir Khuller, David M. Mount, and Giri Narasimhan. Algorithms for facility location problems with outliers. In Proceedings of the Twelfth Annual Symposium on Discrete Algorithms, January 7-9, 2001, Washington, DC, USA, pages 642-651. ACM/SIAM, 2001.
-
Ke Chen. A constant factor approximation algorithm for k-median clustering with outliers. In SODA, pages 826-835, 2008.
- Zachary Friggstad, Kamyar Khodamoradi, Mohsen Rezapour, and Mohammad R. Salavatipour. Approximation schemes for clustering with outliers. ACM Trans. Algorithms, 15(2):26:1-26:26, 2019. URL: https://doi.org/10.1145/3301446.
- Fabrizio Grandoni, R. Ravi, Mohit Singh, and Rico Zenklusen. New approaches to multi-objective optimization. Math. Program., 146(1-2):525-554, 2014. URL: https://doi.org/10.1007/s10107-013-0703-7.
- Anupam Gupta, Benjamin Moseley, and Rudy Zhou. Structural Iterative Rounding for Generalized k-Median Problems. arXiv e-prints, page arXiv:2009.00808, 2020. URL: http://arxiv.org/abs/2009.00808.
-
Sungjin Im, Mahshid Montazer Qaem, Benjamin Moseley, Xiaorui Sun, and Rudy Zhou. Fast noise removal for k-means clustering. In The 23rd International Conference on Artificial Intelligence and Statistics, AISTATS 2020, 26-28 August 2020, Online [Palermo, Sicily, Italy], pages 456-466, 2020.
- Kamal Jain and Vijay V. Vazirani. Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation. J. ACM, 48(2):274-296, 2001. URL: https://doi.org/10.1145/375827.375845.
- Ravishankar Krishnaswamy, Amit Kumar, Viswanath Nagarajan, Yogish Sabharwal, and Barna Saha. Facility location with matroid or knapsack constraints. Math. Oper. Res., 40(2):446-459, 2015. URL: https://doi.org/10.1287/moor.2014.0678.
- 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, STOC 2018, Los Angeles, CA, USA, June 25-29, 2018, pages 646-659. ACM, 2018. URL: https://doi.org/10.1145/3188745.3188882.
- Shi Li and Ola Svensson. Approximating k-median via pseudo-approximation. SIAM J. Comput., 45(2):530-547, 2016. URL: https://doi.org/10.1137/130938645.