Abstract
We consider the metric uncapacitated facility location problem(UFL). In this paper we modify the (1 + 2/e)-approximation algorithm of Chudak and Shmoys to obtain a new (1.6774,1.3738)- approximation algorithm for the UFL problem. Our linear programing rounding algorithm is the first one that touches the approximability limit curve \((\gamma_f, 1+2e^{-\gamma_f})\) established by Jain et al. As a consequence, we obtain the first optimal approximation algorithm for instances dominated by connection costs.
Our new algorithm - when combined with a (1.11,1.7764)-approxima- tion algorithm proposed by Jain, Mahdian and Saberi, and later analyzed by Mahdian, Ye and Zhang - gives a 1.5-approximation algorithm for the metric UFL problem. This algorithm improves over the previously best known 1.52-approximation algorithm by Mahdian, Ye and Zhang, and it cuts the gap with the approximability lower bound by 1/3.
The algorithm is also used to improve the approximation ratio for the 3-level version of the problem.
Keywords
- Approximation Algorithm
- Cluster Center
- Facility Location Problem
- Linear Programing Relaxation
- Fractional Solution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Byrka, J. (2007). An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_3
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DOI: https://doi.org/10.1007/978-3-540-74208-1_3
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