A review of hierarchical facility location models
Computers and Operations Research
A new approximation algorithm for the multilevel facility location problem
Discrete Applied Mathematics
An approximation algorithm for the k-level capacitated facility location problem
Journal of Combinatorial Optimization
A primal-dual approximation algorithm for the k-level stochastic facility location problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Computers and Operations Research
Inapproximability of the multi-level uncapacitated facility location problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved approximation algorithms for the robust fault-tolerant facility location problem
Information Processing Letters
An approximation algorithm for the k-level stochastic facility location problem
Operations Research Letters
Approximation algorithm for facility location with service installation costs
Operations Research Letters
Improved LP-rounding approximation algorithm for k-level uncapacitated facility location
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Computers and Industrial Engineering
| Hi-index | 0.00 |
In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [A. A. Ageev, Oper. Res. Lett., 30 (2002), pp. 327--332], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k \ge 2, thus improving the previous bound of 4.56 achieved by a combinatorial algorithm. 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 $\infty$. The values of h(k) can be easily computed with an arbitrary accuracy: h(2)\approx 2.4211, h(3)\approx 2.8446, h(4)\approx 3.0565, h(5)\approx 3.1678, and so on. Thus, for the cases of k=2 and k=3 the second combinatorial algorithm ensures an approximation factor substantially better than 3, which is currently the best approximation ratio for the k-level problem provided by the noncombinatorial algorithm due to Aardal, Chudak, and Shmoys [Inform. Process. Lett., 72 (1999), pp. 161--167].