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In this paper we design and prove correct a fully dynamic distributedalgorithm for maintaining an approximate Steiner tree that connects via aminimum-weight spanning tree a subset of nodes of a network (referred asSteiner members or Steiner group) . Steiner trees are good candidates toefficiently implement communication primitives such as publish/subscribe ormulticast, essential building blocks for the new emergent networks (e.g. P2P,sensor or adhoc networks). The cost of the solution returned by our algorithmis at most $\log |S|$ times the cost of an optimal solution, where $S$ is thegroup of members. Our algorithm improves over existing solutions in severalways. First, it tolerates the dynamism of both the group members and thenetwork. Next, our algorithm is self-stabilizing, that is, it copes with nodesmemory corruption. Last but not least, our algorithm is\emph{superstabilizing}. That is, while converging to a correct configuration(i.e., a Steiner tree) after a modification of the network, it keeps offeringthe Steiner tree service during the stabilization time to all members that havenot been affected by this modification.

A Superstabilizing $\log(n)$-Approximation Algorithm for Dynamic Steiner Trees