We propose a general framework for boosting combinatorial solvers through human computation. Our framework combines insights from human workers with the power of combinatorial optimization. The combinatorial solver is also used to guide requests for the workers, and thereby obtain the most useful human feedback quickly. Our approach also incorporates a problem decomposition approach with a general strategy for discarding incorrect human input. We apply this framework in the domain of materials discovery, and demonstrate a speedup of over an order of magnitude.