K. Jain et Vv. Vazirani, Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation, J ACM, 48(2), 2001, pp. 274-296
We present approximation algorithms for the metric uncapacitated facility l
ocation problem and the metric k-median problem achieving guarantees of 3 a
nd 6 respectively. The distinguishing feature of our algorithms is their lo
w running time: 0(m log m) and 0(m log m(L + log(n))) respectively, where n
and m are the: total number of vertices and edges in the underlying comple
te bipartite graph on cities and facilities. The main algorithmic ideas are
a new extension of the primal-dual schema and the use of Lagrangian relaxa
tion to derive approximation algorithms.