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Several multicast protocols such as Protocol Independent Multicast (PIM) (Deering et al., 1996) and Core-Based Trees (CBT) (Ballardie et al., 1993) use the notion of group-shared trees. The reason is that construction of minimal-cost tree spanning all members of the multicast group is expensive, hence these protocols use a core-based group-shared tree to distribute packets from all the sources. A core-based tree is a shortest-path tree rooted at some core node. The core node is also referred to as a center node or a rendezvous point. Core nodes may be chosen from some preselected set of nodes or some heuristics may be employed to select core nodes. We present distributed core selection and migration protocols for mobile ad hoc networks with dynamically changing network topology. Most protocols for core selection in static networks are not suitable for ad hoc networks, since these algorithms depend on knowledge of entire network topology, which is not available or is too expensive to maintain in an ad hoc network with dynamic topology. The proposed core location method is based on the notion of median node of the current multicast tree instead of the median node of the entire network. The rationale is that the mobile ad hoc network graphs are in general sparse and, hence, the multicast tree is a good approximation of the entire network for the current purpose. Our adaptive distributed core selection and migration method uses the fact that the median of a tree is equivalent to the centroid of that tree. The significance of this observation is due to the fact that the computation of a tree's centroids does not require any distance information. Mobile ad hoc networks have limited bandwidth which needs to be conserved. Hence, we use the cost of multicast tree as the sum of weights of all the links in the tree, which signifies the total bandwidth consumed for multicasting a packet. We compare the cost of shortest-path tree rooted at the tree median, CostTM, with the cost of shortest-path tree rooted at the median of the graph, CostGM, which requires complete topology information to compute. A network graph model for generating random ad hoc mobile networks is developed to perform this comparison. The simulation results show that for large size networks- , the ratio CostTM/CostGM lies between 0.8 to 1.2 for different multicast groups. Further, as the size of the multicast group increases the ratio approaches 1.