Abstract
hierarchical clustering is an important problem with wide applications. In this paper, we approach the problem with a formulation based on weighted graphs and introduce new algorithmic techniques. Our new formulation and techniques lead to new kernelization algorithms and parameterized algorithms for the problem, which significantly improve previous algorithms for the problem.
Supported in part by the US NSF under the Grants CCF-0830455 and CCF-0917288.
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References
Agarwala, R., Bafna, V., Farach, M., Paterson, M., Thorup, M.: On the approximability of numerical taxonomy (fitting distances by tree metrics). SIAM J. Comput. 28(3), 1073–1085 (1999)
Ailon, N., Charikar, M.: Fitting tree metrics: hierarchical clustering and phylogeny. SIAM J. Comput. 40(5), 1275–1291 (2011)
Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM 55(5), Article 23, 1–27 (2008)
Böcker, S.: A golden ratio parameterized algorithm for cluster editing. J. Discret Algorithms 16, 79–89 (2012)
Böcker, S., Briesemeister, S., Bui, Q., Truss, A.: Going weighted: parameterized algorithms for cluster editing. Theor. Comput. Sci. 410, 5467–5480 (2009)
Cao, Y., Chen, J.: Cluster editing: kernelization based on edge cuts. Algorithmica 64, 152–169 (2012)
Chen, J., Meng, J.: A 2k kernel for the cluster editing problem. Journal of Computer and System Sciences 78, 211–220 (2012)
Gan, G., Ma, C., Wu, J.: Data Clustering: Theory, Algorithms, and Applications. ASASIAM Series on Statistics and Applied Probability. SIAM (2007)
Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410, 718–726 (2009)
Guo, J., Hartung, S., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Exact algorithms and experiments for hierarchical tree clustering. In: Proc. 24th AAAI Conference on Artificial Intelligence, AAAI 2010, pp. 457–462 (2010)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, New York (1997)
Jain, A., Murty, M., Flynn, P.: Data clustering: a review. ACM Comput. Surv. 31, 264–323 (1999)
Krivanek, M., Moravek, J.: NP-hard problems in hierarchical-tree clustering. Acta Informatica 23(3), 311–323 (1986)
Larose, D.: Discovering Knowledge in Data: An Introduction to Data Mining. John Wiley & Sons (2005)
Manning, C., Raghavan, P., Schütze, H.: Introduction to Information Retrieval. Cambridge University Press (2008)
Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144, 173–182 (2004)
van Zuylen, A., Williamson, D.: Deterministic pivoting algorithms for constrained ranking and clustering problems. Mathematics of Operations Research 34(3), 594–620 (2009)
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Cao, Y., Chen, J. (2013). On Parameterized and Kernelization Algorithms for the Hierarchical Clustering Problem. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_29
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DOI: https://doi.org/10.1007/978-3-642-38236-9_29
Publisher Name: Springer, Berlin, Heidelberg
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