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.
CITATION STYLE
Byrka, J., Pensyl, T., Rybicki, B., Spoerhase, J., Srinivasan, A., & Trinh, K. (2015). An improved approximation algorithm for knapsack median using sparsification. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9294, pp. 275–287). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_24
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