Three factors are driving the demand for rapid FPGA compilation. First, as FPGAs have grown in logic capacity, the compile computation has grown more quickly than the compute power of the available computers. Second, there exists a subset of users who are willing to pay for very high speed compile with a decrease in quality of result, and accordingly being required to use a larger FPGA or use more real-estate on a given FPGA than is otherwise necessary. Third, very high speed compile has been a long-standing desire of those using FPGA-based custom computing machines, as they want compile times at least closer to those of regular computers. This paper focuses on the routing phase of the compile process, and in particular on routability-driven routing (as opposed to timing-driven routing). We present a routing algorithm and routing tool that has three unique capabilities relating to very high-speed compile: 1. For a “low stress ” routing problem (which we define as the case where the track supply is at least 10 % greater than the minimum number of tracks per channel actually needed to route a circuit) the routing time is very fast. For example, the routing phase (after the netlist is parsed and the routing graph is constructed) for a 20,000 LUT/FF pair circuit with 30 % extra tracks is only 23 seconds on a 300 MHz Sparcstation. 2. For low-stress routing problems the routing time is nearlinear in the size of the circuit, and the linearity constant is very small: 1.1 ms per LUT/FF pair, or roughly 55,000 LUT/FF pairs per minute. 3. For more difficult routing problems (where the track supply is close to the minimum needed) we provide a method that quickly identifies and subdivides this class into two sub-classes: (i) those circuits which are difficult (but possible) to route and will take significantly more time than low-stress problems, and (ii) those circuits which are impossible to route. In the first case the user can choose to continue or reduce the amount of logic; in the second case the user is forced to reduce the amount of logic or obtain a larger FPGA. 1.