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Three dimensional Networks-on-Chip (3D NoCs) have evolved as an ideal solution to the communication demands and complexity of future high density many core architectures. However, the design practicality of 3D NoCs faces several challenges such as thermal issues, high power consumption and area overhead of 3D routers as well as high complexity and cost of vertical link implementation. To mitigate the performance and manufacturing cost of 3D NoCs, inhomogeneous architectures have emerged to combine 2D and 3D routers in 3D NoCs producing lower area and energy consumption while maintaining the performance of homogeneous 3D NoCs. Due to the limited number of vertical links, application mapping on inhomogeneous 3D NoCs can be complex. However, application mapping has a great impact on the performance and energy consumption of NoCs. This paper presents an energy and performance aware application mapping algorithm for inhomogeneous 3D NoCs. The algorithm has been evaluated with various realistic traffic patterns and compared with existing mapping algorithms. Experimental results show NoCs mapped with the proposed algorithm have lower energy consumption and significant reduction in packet delays compared to the existing algorithms and comparable average packet latency with Branch-and-Bound. [ABSTRACT FROM AUTHOR]