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When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

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posted on 01.02.1987 by Ajit Agrawal, Philip Klein, Ramamoorthi Ravi
We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with link-costs and, for each pair {i, j} of nodes, an edge connectivity requirement rij. The goal is to find a minimum-cost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2[log2(r + 1)] of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial min-max approximate equality relating minimum-cost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.

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01/02/1987

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