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.
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