# The Single-Sink Buy-at-Bulk LP Has Constant Integrality Gap

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## Abstract

The buy-at-bulk network design problem is to design a minimum cost network to satisfy some flow demands, by installing cables from an available set of cables with different costs per unit length and capacities, where the cable costs obey economies of scale. For the single-sink buy-at-bulk problem, [10] gave the first constant factor approximation. In this paper, we use techniques of [9] to get an improved constant factor approximation. This also shows that the integrality gap of a natural linear programming formulation is a constant, thus answering the open question in [9].

## Keywords

Steiner Tree Network Design Problem Annual IEEE Symposium Constant Factor Approximation Building Cost
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