Accelerating a continuous-time analog SAT solver using GPUs

Recently, a continuous-time, deterministic analog solver based on ordinary differential equations (CTDS) was introduced, to solve Boolean satisfiability (SAT), a family of discrete constraint satisfaction problems. Since SAT is NP-complete, efficient algorithms would benefit solving a large number of decision type problems, both within industry and the sciences. Here we present a graphics processing units (GPU) based implementation of the CTDS and its variants and show that one can achieve significantly improved performance within a wide range of SAT problems. We present and discuss three versions of our GPU implementation and compare their performance to CPU implementations, showing an improvement factor of up to two orders of magnitude. We illustrate the performance of our GPU-based solver on random SAT problems and a notoriously difficult graph coloring problem, the Ramsey number problem R(3,3,3,3), and compare it with the state-of-the-art SAT solver MiniSAT’s performances on CPUs.