Abstract
The lower-bounded k-median problem considers a set C of clients, a set F of facilities, and a parameter B, the goal is to open k facilities and connect each client to an opened facility, such that each opened facility is connected with at least B clients and the total connection cost is minimized. The problem is known to admit an O(1)-approximation algorithm, while the constant is implicit and seems to be a very large constant. In this paper, we give an approach that converts the lower-bounded k-median problem to the capacitated facility location problem, which yields a \((516+\epsilon )\)-approximation for the lower-bounded k-median problem.
This work was supported by National Natural Science Foundation of China (61672536, 61872450, 61828205, and 61802441), Hunan Provincial Key Lab on Bioinformatics, and Hunan Provincial Science and Technology Program (2018WK4001).
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Guo, Y., Huang, J., Zhang, Z. (2020). A Constant Factor Approximation for Lower-Bounded k-Median. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_11
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DOI: https://doi.org/10.1007/978-3-030-59267-7_11
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