Network-on-chip (NoC) architectures with optimized topologies have been shown to be superior to regular architectures (such as mesh) for application specific multiprocessor system-on-chip (MPSoC) devices. The application specific NoC design problem takes as input the system-level floorplan of the computation architecture, characterized library of NoC components, and the communication performance requirements. The objective is to generate an optimized NoC topology, and routes for the communication traces on the architecture such that the performance requirements are satisfied and power consumption is minimized. The paper discusses a two stage automated approach consisting of i) core to router mapping, and ii) topology and route generation for design of custom NoC architectures. In particular it presents an optimal technique for core to router mapping (stage i), and a factor 2 approximation algorithm for custom topology generation (stage ii). The superior quality of the techniques is established by experimentation with benchmark applications, and comparisons with integer linear programming (ILP) formulations, and heuristic techniques.