We study a network loading 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 flows 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 minimum Steiner tree. When all sources have the same demand value, the ratio improves to (ρST +1) and in particular, to 2 when all nodes in the graph are sources.
['Refael Hassin', 'R. Ravi', 'F. S. Salman']
Approximation algorithms for a capacitated network design problem