On the integrality gap of a natural formulation of the single-sink buy-at-bulk network design problem

Abstract

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.