Some embodiments provide techniques and systems for routing nets in a circuit design in parallel. During operation, the system can receive a set of partitions for a circuit design, wherein each partition has zero or more overlapping partitions along four directions, e.g., up, down, left, and right. Next, the system can perform, in parallel, detailed routing on non-overlapping partitions in the set of partitions, wherein detailed routing is performed on a partition after detailed routing is completed on adjacent or overlapping partitions that located along two perpendicular directions. In some embodiments, each detailed routing thread that is executing in parallel performs detailed routing on a different net.