Abstract
The buy-at-bulk network design problem has been extensively studied in the general graph model. In this paper we consider the geometric version of the problem, where all points in a Euclidean space are candidates for network nodes. We present the first general approach for geometric versions of basic variants of the buy-at-bulk network design problem. It enables us to obtain quasi-polynomial-time approximation schemes for basic variants of the buy-at-bulk geometric network design problem with polynomial total demand. Then, for instances with few sinks and low capacity links, we design very fast polynomial-time low-constant approximations algorithms.
Research supported in part by VR grant 621-2005-4085, the Royal Society IJP - 2006/R2, the Centre for Discrete Mathematics and its Applications, the Special Coordination Funds for Promoting Science and Technology (Japan), and the Visby Programme Scholarship 01224/2007.
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Czumaj, A., Czyzowicz, J., Gąsieniec, L., Jansson, J., Lingas, A., Zylinski, P. (2009). Approximation Algorithms for Buy-at-Bulk Geometric Network Design. In: Dehne, F., Gavrilova, M., Sack, JR., Tóth , C.D. (eds) Algorithms and Data Structures. WADS 2009. Lecture Notes in Computer Science, vol 5664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03367-4_15
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DOI: https://doi.org/10.1007/978-3-642-03367-4_15
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