A detailed routing algorithm, called the coarse graph expander (CGE), that has been designed specifically for field-programmable gate arrays (FPGAs) is described. The algorithm approaches this problem in a general way, allowing it to be used over a wide range of different FPGA routing architectures. It addresses the issue of scarce routing resources by considering the side effects that the routing of one connection has on another, and also has the ability to optimize the routing delays of time-critical connections. CGE has been used to obtain excellent routing results for several industrial circuits implemented in FPGAs with various routing architectures. The results show that CGE can route relatively large FPGAs in very close to the minimum number of tracks as determined by global routing, and it can successfully optimize the routing delays of time-critical connections. CGE has a linear run time over circuit size. >