Motivation: We introduce SneakySnake, a highly parallel and highly accurate pre-alignment filter that remarkably reduces the need for computationally costly sequence alignment. The key idea of SneakySnake is to reduce the approximate string matching (ASM) problem to the single net routing (SNR) problem in VLSI chip layout. In the SNR problem, we are interested in finding the optimal path that connects two terminals with the least routing cost on a special grid layout that contains obstacles. The SneakySnake algorithm quickly solves the SNR problem and uses the found optimal path to decide whether or not performing sequence alignment is necessary. Reducing the ASM problem into SNR also makes SneakySnake efficient to implement on CPUs, GPUs, and FPGAs. Results: SneakySnake significantly improves the accuracy of pre-alignment filtering by up to four orders of magnitude compared to the state-of-the-art pre-alignment filters, Shouji, GateKeeper, and SHD. For short sequences, SneakySnake accelerates Edlib (state-of-the-art implementation of Myers's bit-vector algorithm) and Parasail (state-of-the-art sequence aligner with a configurable scoring function), by up to 37.7x and 43.9x (>12x on average), respectively, with its CPU implementation, and by up to 413x and 689x (>400x on average), respectively, with FPGA and GPU acceleration. For long sequences, the CPU implementation of SneakySnake accelerates Parasail and KSW2 (sequence aligner of minimap2) by up to 979x (276.9x on average) and 91.7x (31.7x on average), respectively. As SneakySnake does not replace sequence alignment, users can still obtain all capabilities (e.g., configurable scoring functions) of the aligner of their choice, unlike existing acceleration efforts that sacrifice some aligner capabilities. Availability: https://github.com/CMU-SAFARI/SneakySnake