Abstract
We consider the uncapacitated facility location problem. In this problem, there is a set of locations at which facilities can be built; a fixed cost f i is incurred if a facility is opened at location i. Further- more, there is a set of demand locations to be serviced by the opened facilities; if the demand location j is assigned to a facility at location i, then there is an associated service cost of cij. The objective is to de- termine which facilities to open and an assignment of demand points to the opened facilities, so as to minimize the total cost. We assume that the service costs c ij are symmetric and satisfy the triangle inequality. For this problem we obtain a (1 + 2/e)-approximation algorithm, where 1 + 2/e ≈ 1.736, which is a significant improvement on the previously known approximation guarantees.
The algorithm works by rounding an optimal fractional solution to a linear programming relaxation. Our techniques use properties of opti- mal solutions to the linear program, randomized rounding, as well as a generalization of the decomposition techniques of Shmoys, Tardos, and Aardal.
Research partially supported by NSF grants DMS-9505155 and CCR-9700029 and by ONR grant N00014-96-1-00500.
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Chudak, F.A. (1998). Improved Approximation Algorithms for Uncapacitated Facility Location. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_14
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DOI: https://doi.org/10.1007/3-540-69346-7_14
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