A method, system, computer system, and computer program product including an algorithm that performs the constraints-based global routing step in the physical design of integrated circuits. The algorithm is based on finding routes for the entire circuit based on constraints being satisfied for the entire design. Initially, for each net, a set of possible routing solutions is determined based on applicable constraints. The possible solutions for the nets are combined to create a highly-connected “intersection graph,” with each intersection graph node representing a net. The intersection graph is partitioned based on constraints and performance criteria. An optimal solution is determined for each partition. The optimal solutions for the partitions are then combined to produce a global routing solution. The global routing solution is provided to a detailed router, which completes the routing for the design.