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A constant factor approximation for the single sink edge installation problems

We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(\log |R|), where R is the set of sources. Our algorithms are combinatorial and can be derandomized easily at the cost of a constant factor loss in the approximation ratio.