Script of Lecture 7 , Approximation Algorithms Summer term 2017

1 The Uncapacitated Facility Location Problem Input: a set D of demands (or clients); a set F of facilities; for each client j ∈ D and facility i ∈ F , there is a cost cij of assigning client j to facility i; and there is a cost fi associated with each facility i ∈ F . Output: Choose a subset of facilities F ′ ⊆ F which minimizes the total cost of facilities in F ′ plus the total cost of assigning each client to the nearest facility in F ′, i. e., ∑ i∈F ′ fi + ∑ j∈D mini∈F ′ cij . (The first term is called the facility cost, and the second term is called the assignment cost.)