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

  • Authors:
  • Kamal Jain;Vijay V. Vazirani

  • Affiliations:
  • College of Computing, Georgia Institute of Technology, Atlanta, GA;College of Computing, Georgia Institute of Technology, Atlanta, GA

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2001

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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.