Determining a sequence of stable multicast Steiner trees in mobile ad hoc networks

We show that given the complete knowledge of future topology changes, it is possible to determine the sequence of stable multicast Steiner trees (called the stable mobile multicast Steiner tree) in a multicast session such that the number of tree transitions is minimal. The algorithm to determine the stable mobile multicast Steiner tree and the minimum number of tree transitions is called OptTreeTrans. It is based on the following greedy approach: whenever a multicast Steiner tree is required, choose the Steiner tree that will exist for the longest time. The above strategy is repeated over the duration of the multicast session. We prove that OptTreeTrans gives the optimal number of tree transitions and simultaneously yields the stable mobile multicast Steiner tree. We study the performance of OptTreeTrans in terms of the number of tree transitions and the number of links constituting the Steiner tree for different conditions of node mobility and network density.