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This paper proposes a new problem called the dynamic Steiner tree problem. Interest in the dynamic Steiner tree problem is motivated by multipoint routing in communication networks, where the set of nodes in the connection changes over time. This problem, which has its basis in the Steiner tree problem on graphs, can be divided into two cases: one in which rearrangement ofexisting routes is not allowed, and a second in which rearrangement is allowed.For the nonrearrangeable version, it is shown that the worst-case performance for any algorithm is at least lg n times the cost of an optimum solution with complete rearrangement. Here n is the maximum number of nodes to be connected. In addition, a simple, polynomial time algorithm is present that has worst-case performance within two times this bound. In the rearrangeable case, a polynomial time algorithm is presented with worst-case performance bounded by a constant times optimum.

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In this paper, we prove that the worst case performance of the Steiner tree approximation algorithm by Rayward-Smith is within two times optimal and that two is the best bound in the sense that there are instances for which RS will do worse than any value less than two.

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