FPGA placement and routing is time consuming, often serving as the major obstacle inhibiting a fast edit-compile-test loop in prototyping and development and the major obstacle preventing late-bound hardware and design mapping for reconfigurable systems. We introduce a stochastic search scheme which can achieve comparable route quality to traditional, software-based routers while being amenable to parallel, spatial implementation. We quantify the quality and performance of this route scheme using the Toronto Place-andRoute Challenge benchmarks. We sketch hardware implementations ranging from a minimal hardware-search assistance scheme which provides two orders of magnitude speedup, to FPGA-based schemes which provide greater speedup, to full hardware schemes which provide over three orders of magnitude routing acceleration. For coarse-grained devices with wide-word datapaths, the area overhead for integrating this hardware support into the network can be below 30%; for conventional FP...