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The increasing complexity of interconnection designs has enhanced the importance of research into global routing when seeking high-routability (low overflow) results or rapid search paths that report wirelength estimations to a placer. This work presents two routing techniques, namely circular fixed-ordering monotonic routing and evolution-based rip-up and rerouting using a two-stage cost function in a high-performance congestion-driven 2-D global router. We also propose two efficient via-minimization methods, namely congestion relaxation by layer shifting and rip-up and reassignment, for a dynamic programming-based layer assignment. Experimental results demonstrate that our router achieves performance similar to the first two winning routers in ISPD 2008 Routing Contest in terms of both routability and wirelength at a 1.05 × and 18.47 × faster routing speed. Moreover, the proposed layer assignment achieves fewer vias and shorter wirelength than congestion-constrained layer assignment (COLA).