Speeding Up Constrained k-Means Through 2-Means
Document Type
Conference Proceeding
Publication Date
9-19-2024
Abstract
For the constrained 2-means problem, we present a O\left( dn+ d({1\over \epsilon })^{O({1\over \epsilon })}\log n\right)O\left( dn+ d({1\over \epsilon })^{O({1\over \epsilon })}\log n\right) time algorithm. It generates a collection U of approximate center pairs (c_1, c_2) such that one of pairs in U can induce a (1+\epsilon )-approximation for the problem. The existing approximation scheme for the constrained 2-means problem takes O(({1\over \epsilon })^{O({1\over \epsilon })}dn) time, and the existing approximation scheme for the constrained k-means problem takes O(({k\over \epsilon })^{O({k\over \epsilon })}dn) time. Using the method developed in this paper, we point out that every existing approximating scheme for the constrained k-means so far with time C(k, n, d, \epsilon ) can be transformed to a new approximation scheme with time complexity {C(k, n, d, \epsilon )/ k^{\varOmega ({1\over \epsilon })}}.
Recommended Citation
Feng, Q., Fu, B. (2024). Speeding Up Constrained k-Means Through 2-Means. In: Ghosh, S., Zhang, Z. (eds) Algorithmic Aspects in Information and Management. AAIM 2024. Lecture Notes in Computer Science, vol 15180. Springer, Singapore. https://doi.org/10.1007/978-981-97-7801-0_5
Publication Title
Algorithmic Aspects in Information and Management
DOI
https://doi.org/10.1007/978-981-97-7801-0_5
Comments
© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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