Asymmetric Multicore Processors (AMP) are a very promising architecture to deal efficiently with the wide diversity of applications. In real-time application domains, in-time approximated results are preferred than accurate – but too late – results. In this work, we propose a deployment approach that exploits the heterogeneity provided by AMP architectures and the approximation tolerance provided by the applications, so as to increase as much as possible the quality of the results under given energy and timing constraints. Initially, an optimal approach is proposed based on problem linearization and decomposition. Then, a heuristic approach is developed based on iteration relaxation of the optimal version. The obtained results show 16.3% reduction in the computation time for the optimal approach compared to the conventional optimal approaches. The proposed heuristic approach is about 100 times faster at the cost of a 29.8% QoS degradation in comparison with the optimal solution.