Abstract
We study problems that integrate buy-at-bulk network design into the classical (connected) facility location problem. In such problems, we need to open facilities, build a routing network, and route every client demand to an open facility. Furthermore, capacities of the edges can be purchased in discrete units from K different cable types with costs that satisfy economies of scale. We extend the linear programming framework of Talwar [IPCO 2002] for the single-source buy-at-bulk problem to these variants and prove integrality gap upper bounds for both facility location and connected facility location buy-at-bulk problems. For the unconnected variant we prove an integrality gap bound of O(K), and for the connected version, we get an improved bound of O(1).
M. Rezapour—Supported by the Deutsche Forschungsgemeinschaft within the research training group ‘Methods for Discrete Structures’ (GRK 1408).
M.R. Salavatipour—Supported by NSERC.
J.A. Soto—Partially supported by FONDECYT grant 11130266 (Chile) and by Núcleo Milenio Información y Coordinación en Redes ICM/FIC RC130003.
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Friggstad, Z., Rezapour, M., Salavatipour, M.R., Soto, J.A. (2015). LP-Based Approximation Algorithms for Facility Location in Buy-at-Bulk Network Design. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_31
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DOI: https://doi.org/10.1007/978-3-319-21840-3_31
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