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In this paper, we propose a novel mapping algorithm for providing Quality of Service (QoS) under bandwidth constraints in 3D Network-on-Chip (NoC). The QoS is warranted in such a way that all minimum feasible paths considering the required and available bandwidth are explored by the mapping algorithm. The maximum required bandwidth on the network links for this mapping algorithm is compared with other methods such as NMAP, Onyx and Citrine while applied on two video processing applications i.e. VOPD (Video Object Plane Decoder) and MPEG-4. The available bandwidth of vertical and horizontal links are considered the same and different in the experimental results.