A combinatorial approximation algorithm for k-level facility location problem with submodular penalties

We present an improved approximation algorithm for k -level facility location problem with submodular penalties, the new approximation ratio is 2.9444 for any constant k , which improves the current best approximation ratio 3.314. The central ideas in our results are as follows: first, we restructure the problem as an uncapacitated facility location problem, then we use the primal-dual scheme with greedy augmentation. The key technique of our result is that we change the way of last opening facility set in primal-dual approximation algorithm to get much more tight result for k -level facility location problem with submodular penalties.