Abstract
Knapsack median is a generalization of the classic k-median problem in which we replace the cardinality constraint with a knapsack constraint. It is currently known to be 32-approximable. We improve on the best known algorithms in several ways, including adding randomization and applying sparsification as a preprocessing step. The latter improvement produces the first LP for this problem with bounded integrality gap. The new algorithm obtains an approximation factor of 17.46. We also give a 3.05 approximation with small budget violation.
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Byrka, J., Pensyl, T., Rybicki, B., Spoerhase, J., Srinivasan, A., Trinh, K. (2015). An Improved Approximation Algorithm for Knapsack Median Using Sparsification. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_24
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DOI: https://doi.org/10.1007/978-3-662-48350-3_24
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