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# Lagrangian Relaxation for the k-Median Problem: New Insights and Continuity Properties

@inproceedings{Archer2003LagrangianRF, title={Lagrangian Relaxation for the k-Median Problem: New Insights and Continuity Properties}, author={Aaron Archer and Ranjithkumar Rajagopalan and David B. Shmoys}, booktitle={ESA}, year={2003} }

- Published 2003 in ESA
DOI:10.1007/978-3-540-39658-1_6

This work gives new insight into two well-known approximation algorithms for the uncapacitated facility location problem: the primal-dual algorith m of Jain & Vazirani, and an algorithm of Mettu & Plaxton. Our main result answ er positively a question posed by Jain & Vazirani of whether their algorithm ca n be modified to attain a desired “continuity” property. This yields an upper boun d of 3 on the integrality gap of the natural LP relaxation of the k-median problem, but our approach does not… CONTINUE READING

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