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We study the problem of controlling data overhead of mesh-based multicast ad hoc routing protocols by adaptively adding redundancy to the minimal data overhead multicast mesh as required by the network conditions. We show that the computation of the minimal data overhead multicast mesh is NP-complete, and we propose an heuristic approximation algorithm inspired on epidemic algorithms. In addition, we propose a mobility-aware and adaptive mesh construction algorithm based on a probabilistic path selection being able to adapt the reliability of the multicast mesh to the mobility of the network. Our simulation results show that the proposed approach, when implemented into ODMRP, is able to offer similar performance results and a lower average latency while reducing data overhead between 25 to 50% compared to the original ODMRP.