Abstract
We study a capacitated network design problem with applications in local access network design. Given a network, the problem is to route flow from several sources to a sink and to install capacity on the edges to support the flow at minimum cost. Capacity can be purchased only in multiples of a fixed quantity. All the flow from a source must be routed in a single path to the sink. This NP-hard problem generalizes the Steiner tree problem and also more effectively models the applications traditionally formulated as capacitated tree problems. We present an approximation algorithm with performance ratio (ρST + 2) where ρST is the performance ratio of any approximation algorithm for the minimum Steiner tree problem. When all sources have unit demand, the ratio improves to ρST + 1) and, in particular, to 2 when all nodes in the graph are sources.
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Hassin, R., Ravi, R. & Salman, F. Approximation Algorithms for a Capacitated Network Design Problem. Algorithmica 38, 417–431 (2004). https://doi.org/10.1007/s00453-003-1069-7
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DOI: https://doi.org/10.1007/s00453-003-1069-7