Networks on Chip (NoCs) have been shown as an efficient solution to the complex on-chip communication problems derived from the increasing number of processor cores. One of the key issues in the design of NoCs is the reduction of both area and power dissipation. As a result, two-dimensional meshes have become the preferred topology, since it offers low and constant link delay. Unfortunately, manufacturing defects or even real-time failures often make the resulting topology to become irregular, preventing the use of traditional routing algorithms. This scenario shows the need for topology-agnostic routing algorithms that provide a valid routing solution when applied over any topology. This paper proposes a new communication-driven routing technique that optimizes the network performance for Application-Specific NoCs. This technique combines a flexible, topology-agnostic routing algorithm with a communication-aware mapping technique that matches the traffic generated by the application with the available network bandwidth. Since the mapping technique can be pruned as needed in order to fit either quality function values or time constraints, this technique can be adapted to fit with different computational costs. The evaluation results show that it significantly improves network performance in terms of both latency and power consumption.