We will look at a greedy algorithm for the uncapacitated facility location problem. It has a similar flavor to the approximation algorithm for set cover, in that it uses the method of dual fitting. The greedy approach yields some of the strongest results for the facility location problem. The algorithm presented here has an approximation factor of 1.61 and is due to Jain et al. [1]. The best kn...

A spreading metric on the graph G for a given MLA problem instance is an assignment, δ : E → Q, of lengths to the edges of the graph that has the following properties: • The volume of a spreading metric, ∑ (i,j)∈E δi,jwi,j, of graph G in the MLA problem instance provides a lower bound on the value of the optimal solution of the MLA problem. • It “spreads apart” (w.r.t. metric lengths) the nontr...