Greedy Facility Location Algorithms Analyzed using Dual Fitting with   Factor-Revealing LP
  In this paper, we will formalize the method of dual fitting and the idea of factor-revealing LP. This combination is used to design and analyze two greedy algorithms for the metric uncapacitated facility location problem. Their approximation factors are 1.861 and 1.61, with running times of O(mlog m) and O(n^3), respectively, where n is the total number of vertices and m is the number of edges in the underlying complete bipartite graph between cities and facilities. The algorithms are used to improve recent results for several variants of the problem. 
Kamal Jain and Mohammad Mahdian and Evangelos Markakis and Amin Saberi   and Vijay V. Vazirani