Abstract
Consider the problem of finding a point in a metric space \((\{1,2,\ldots ,n\},d)\) with the minimum average distance to other points. We show that this problem has no deterministic \(o(n^{1+1/(h-1)})\)-query \((2h-\epsilon )\)-approximation algorithms for any constants \(h\in \mathbb {Z}^+\setminus \{1\}\) and \(\epsilon >0\).
C.-L. Chang—Supported in part by the Ministry of Science and Technology of Taiwan under grant 103-2221-E-155-026-MY2.
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References
Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for \(k\)-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)
Chang, C.-L.: A deterministic sublinear-time nonadaptive algorithm for metric \(1\)-median selection. To appear in Theoretical Computer Science
Chang, C.-L.: Some results on approximate \(1\)-median selection in metric spaces. Theor. Comput. Sci. 426, 1–12 (2012)
Chang, C.-L.: Deterministic sublinear-time approximations for metric \(1\)-median selection. Inf. Process. Lett. 113(8), 288–292 (2013)
Chang, C.-L.: A lower bound for metric \(1\)-median selection. Technical report. arXiv:1401.2195 (2014)
Chen, K.: On coresets for \(k\)-median and \(k\)-means clustering in metric and Euclidean spaces and their applications. SIAM J. Comput. 39(3), 923–947 (2009)
Guha, S., Meyerson, A., Mishra, N., Motwani, R., O’Callaghan, L.: Clustering data streams: theory and practice. IEEE Trans. Knowl. Data Eng. 15(3), 515–528 (2003)
Indyk, P.: Sublinear time algorithms for metric space problems. In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pp. 428–434 (1999)
Indyk, P.: High-Dimensional Computational Geometry. Ph.D. thesis, Stanford University (2000)
Jaiswal, R., Kumar, A., Sen, S.: A simple \({D}^2\)-sampling based PTAS for \(k\)-means and other clustering problems. In: Proceedings of the 18th Annual International Conference on Computing and Combinatorics, pp. 13–24 (2012)
Kumar, A., Sabharwal, Y., Sen, S.: Linear-time approximation schemes for clustering problems in any dimensions. J. ACM 57(2), 5 (2010)
Mettu, R.R., Plaxton, C.G.: Optimal time bounds for approximate clustering. Mach. Learn. 56(1–3), 35–60 (2004)
Wu, B.-Y.: On approximating metric \(1\)-median in sublinear time. Inf. Process. Lett. 114(4), 163–166 (2014)
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Chang, CL. (2016). Metric 1-Median Selection: Query Complexity vs. Approximation Ratio. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_11
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