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This paper considers two nodes (base station (BS), access gateway (AG)) mobile network architecture based on a all IP infrastructure. We propose to use a multicast tree from an AG to some BS on which mobility could be predicted. The problem is well defined and the complexity proof and reduction are well discussed. We focus on a distributed process to control multicast functionalities in each IP router to obtain a constraint delay multicast tree compatible with the embedded IP routing that minimises the number of used links. After defining the related problem from a graph theory point of view, we show that it is NP-complete and not approximable. Then, we describe a distributed algorithm and we compare its performance to the ones of a proposed centralised algorithm.