Greedy strikes back: improved facility location algorithms
Journal of Algorithms
A 3-approximation algorithm for the k-level uncapacitated facility location problem
Information Processing Letters
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for Metric Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved Approximation Algorithms for Multilevel Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Cost-distance: two metric network design
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hierarchical placement and network design problems
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximating the two-level facility location problem via a quasi-greedy approach
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
SIAM Journal on Computing
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In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [2], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k ≥ 2, thus improving the previous bound of 4.56. Then we develop another combinatorial algorithm that has a better performance guarantee and uses the first algorithm as a subroutine. The latter algorithm can be recursively implemented and achieves a guarantee factor h(k), where h(k) is strictly less than 3.27 for any k and tends to 3.27 as k goes to ∞. The values of h(k) can be easily computed with an arbitrary accuracy: h(2) ≅ 2.4211, h(3) ≅ 2.8446, h(4) ≅ 3.0565, h(5) ≅ 3.1678 and so on. Thus, for the cases of k = 2 and k = 3the second combinatorial algorithm ensures an approximation factor significantly better than 3, which is currently the best approximation ratio for the k-level problem provided by the non-combinatorial algorithm due to Aardal, Chudak, and Shmoys [1].