An Improved Approximation for k-Median and Positive Correlation in Budgeted Optimization
By Jaroslaw Byrka, Thomas W. Pensyl, Bartosz Rybicki, Aravind Srinivasan, Khoa Trinh. 2014
283 citations recorded by the source corpus.
Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to negative correlation properties. However, what if an application naturally calls for dependent rounding on the one hand and desires positive correlation on the other? More generally, we develop algorithms that guarantee the known properties of dependent rounding but also have nearly bestpossible behavior—near-independence, which generalizes positive correlation—on “small” subsets of the variables. The recent breakthrough of Li and Svensson for the classical k-median problem has to handle positive correlation in certain dependent rounding settings, and does so implicitly. We improve upon Li-Svensson’s approximation ratio for k-median from 2.732 + ε to 2.675 + ε by developing an algorithm that improves upon various aspects of their work. Our dependent rounding approach helps us improve the dependence of the runtime on the parameter ε from Li-Svensson’s NO(1/ε2) to NO((1/ε)log(1/ε)).
Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Computer Networks and Communications
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In Computational Theory and Mathematics
- Charles Lyu
- Kamesh Munagala
- Deeparnab Chakrabarty
- Xingyu Chen
- Suman Kalyan Bera
- Brandon Fain
- Maryam Negahbani
In Computer Networks and Communications
Citations in the corpus
- Proportionally Fair Clustering (2019, methodology): “There are constant approximation polynomial time algorithms for both the k-median [24, 8, 2, 29, 6] and k-center objective [19, 33].”
- Fair Algorithms for Clustering (2019, methodology): “e is a (ˆ+2)-approximation algorithm for the LB-(k;p)-CLUSTERING problem that runs in time O(T+ 2kpoly(n)). Using the best known polynomial time algorithm for the k-median problem due to Byrka et al. [16] and best known FPT-algorithm due to Cohen-Addad et al. [28], we get the following corollary. Th”