Lecture 4: Uncapacitated Facility Location
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چکیده
A Simple logarithmic approximation This problem can be formulated as a set cover problem. Given an instance (D,F, f, d) of the facility location problem, it can be transformed into an instance of a set cover problem (X,S, cost) by • setting X = D, and • setting S = {(i, A) : i ∈ F,A ⊆ D}. (i, A) covers elements of the set A. The cost of the set (i, A) is fi + ∑ j∈A dij . We can then use the standard greedy algorithm for set cover: at every iteration, the algorithm chooses the set (i, A) which minimizes
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