Journal ArticleDOI
Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation
Kamal Jain,Vijay V. Vazirani +1 more
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A new extension of the primal-dual schema and the use of Lagrangian relaxation to derive approximation algorithms for the metric uncapacitated facility location problem and the metric k-median problem achieving guarantees of 3 and 6 respectively.Abstract:
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 logm) and O(m logm(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.read more
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