This work gives new insight into two well-known approximation algorithms for the uncapacitated facility location problem: the primal-dual algorithm of Jain & Vazirani, and an algorithm of Mettu & Plaxton. Our main result answers positively a question posed by Jain & Vazirani of whether their algorithm can be modified to attain a desired "continuity" property. This yields an upper bound of 3 on the integrality gap of the natural LP relaxation of the k-median problem, but our approach does not yield a polynomial time algorithm with this guarantee. We also give a new simple proof of the performance guarantee of the Mettu-Plaxton algorithm using LP duality, which suggests a minor modification of the algorithm that makes it Lagrangian-multiplier preserving. © Springer-Verlag 2003.
CITATION STYLE
Archer, A., Rajagopalan, R., & Shmoys, D. B. (2003). Lagrangian relaxation for the k-median problem: New insights and continuity properties. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2832, 31–42. https://doi.org/10.1007/978-3-540-39658-1_6
Mendeley helps you to discover research relevant for your work.