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).
CITATION STYLE
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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9214, pp. 373–385). Springer Verlag. https://doi.org/10.1007/978-3-319-21840-3_31
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