Approximation algorithms for metric facility location and k -Median problems using the primal-dual schema and Lagrangian relaxation

Journal of the ACM - Tập 48 Số 2 - Trang 274-296 - 2001
Kamal Jain1, Vijay V. Vazirani1
1College of Computing, Georgia, Institute of Technology, Atlanta, GA#TAB#

Tóm tắt

We present approximation algorithms for the metric uncapacitated facility location problem and the metric k -median problem achieving guarantees of 3 and 6 respectively. The distinguishing feature of our algorithms is their low running time: O(m log m ) and O(m log m(L + log ( n ))) respectively, where n and m are the total number of vertices and edges in the underlying complete bipartite graph on cities and facilities. The main algorithmic ideas are a new extension of the primal-dual schema and the use of Lagrangian relaxation to derive approximation algorithms.

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