Topological insulators (TI) are becoming one of the most studied classes of novel materials because of their great potential for applications ranging from spintronics to quantum computers. To fully integrate TI materials in electronic devices, high-quality epitaxial single-crystalline phases with sufficiently large bulk bandgaps are necessary. Current efforts have relied mostly on costly and time-consuming trial-and-error procedures. Here we show that by defining a reliable and accessible descriptor (chi) over cap TI, which represents the topological robustness or feasibility of the candidate, and by searching the quantum materials repository aflowlib.org, we have automatically discovered 28 TIs (some of them already known) in five different symmetry families. These include peculiar ternary halides, Cs{Sn, Pb, Ge} {Cl, Br, I}(3), which could have been hardly anticipated without high-throughput means. Our search model, by relying on the significance of repositories in materials development, opens new avenues for the discovery of more TIs in different and unexplored classes of systems.