Algorithmica https://doi.org/10.1007/s00453-018-0458-x LP-Based Approximation Algorithms for Facility Location in Buy-at-Bulk Network Design 1 2 Zachary Friggstad · Mohsen Rezapour · 1 3 Mohammad R. Salavatipour · Jose A. Soto Received: 17 December 2016 / Accepted: 15 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We study problems that integrate buy-at-bulk network design into the classi- cal (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. Further- more, 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 con- nected 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 the ﬁrst LP-based bound of O(1). A preliminary version of this paper appeared in the Proceedings of the 14th International Symposium on Algorithms and Data Structures (WADS) . Z. Friggstad: Supported by NSERC and
Algorithmica – Springer Journals
Published: May 30, 2018
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