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Networks on chips (NoCs) have evolved as the communication design paradigm of future systems on chips (SoCs). In this work we target the NoC design of complex SoCs with heterogeneous processor/memory cores, providing quality-of-service (QoS) for the application. We present an integrated approach to mapping of cores onto NoC topologies and physical planning of NoCs, where the position and size of the cores and network components are computed. Our design methodology automates NoC mapping, physical planning, topology selection, topology optimization and instantiation, bridging an important design gap in building application specific NoCs. We also present a methodology to guarantee QoS for the application during the mapping-physical planning process by satisfying the delay/jitter constraints and real-time constraints of the traffic streams. Experimental studies show large area savings (up to 2×), bandwidth savings (up to 5×) and network component savings (up to 2.2× in buffer count, 3.8× in number of wires, 1.6× in switch ports) compared to traditional design approaches.