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Chip multiprocessors (CMPs) are gaining momentum in the high-performance computing domain. Networks-on-chip (NoCs) are key components of CMP architectures, in that they have to deal with the communication scalability challenge while meeting tight power, area and latency constraints. 2D mesh topologies are usually preferred by designers of general purpose NoCs. However, manufacturing faults may break their regularity. Moreover, resource management frameworks may require the segmentation of the network into irregular regions. Under these conditions, efficient routing becomes a challenge. Although the use of routing tables at switches is flexible, it does not scale in terms of latency and area due to its memory requirements. Logic-based distributed routing (LBDR) is proposed as a new routing method that removes the need for routing tables at all. LBDR enables the implementation of many routing algorithms on most of the practical topologies we may find in the near future in a multi-core system. From an initial topology and routing algorithm, a set of three bits per switch/output port is computed. Evaluation results show that, by using a small logic, LBDR mimics the performance of routing algorithms when implemented with routing tables, both in regular and irregular topologies. LBDR implementation in a real NoC switch is also explored, proving its smooth integration in the architecture and its negligible hardware and performance overhead.