Abstract
This paper considers the diversity-bounded center problems, where we are given a set of points, each of which was colored in one of the \(\omega \) colors, along with integers k and \(l_i\), \(u_i\) for color i, the goal is to select a k-sized center set so as to minimize the maximum distance of a point to its nearest center, and at the same time, meet the requirements that the amount of selected centers with color i must be within \([l_i, u_i]\) for each i. The diversity-bounded clustering with one-side upper bound and lower bound requirement was considered in (Jones et al., 2020) and (Thejaswi et al., 2021), respectively. We combine the difficulties of them and propose the diversity-bounded center problems from both sides, and as the main contribution, we present 3-approximation algorithms for the red-blue as well as the multi-colored version, the complexity of which for the latter problem is parameterized by \(\omega \).
L. Han—Supported by the National Natural Science Foundation of China (No. 12001523). Shuilian Liu and Yicheng Xu are supported by the Fundamental Research Project of Shenzhen City (No. JCYJ20210324102012033). Yong Zhang is supported by the National Natural Science Foundation of China (No. 12071460).
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Han, L., Liu, S., Xu, Y., Zhang, Y. (2022). Approximation Algorithms for Diversity-Bounded Center Problems. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_33
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DOI: https://doi.org/10.1007/978-3-031-20350-3_33
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