We study two versions of the single sink buy-at-bulk network design problem. We are given a network and a single sink, and several sources which demand a certain amount of flow to be routed to the sink. We are also given a finite set of cable types which have different cost characteristics and obey the principle of economies of scale. We wish to construct a minimum cost network to support the demands, using our given cable types. We study a natural integer program formulation of the problem, and show that its integrality gap is O(k), where k is the number of cable types. As a consequence, we also provide an O(k)-approximation algorithm.
CITATION STYLE
Garg, N., Khandekar, R., Konjevod, G., Ravi, R., Salman, F. S., & Sinha, A. (2001). On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2081, pp. 170–184). Springer Verlag. https://doi.org/10.1007/3-540-45535-3_14
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