The spread of ideas in the scientific community is often viewed as a competition, in which good ideas spread further because of greater intrinsic fitness, and publication venue and citation counts correlate with importance and impact. However, relatively little is known about how structural factors influence the spread of ideas, and specifically how where an idea originates might influence how it spreads. Here, we investigate the role of faculty hiring networks, which embody the set of researcher transitions from doctoral to faculty institutions, in shaping the spread of ideas in computer science, and the importance of where in the network an idea originates. We consider comprehensive data on the hiring events of 5032 faculty at all 205 Ph.D.-granting departments of computer science in the U.S. and Canada, and on the timing and titles of 200,476 associated publications. Analyzing five popular research topics, we show empirically that faculty hiring can and does facilitate the spread of ideas in science. Having established such a mechanism, we then analyze its potential consequences using epidemic models to simulate the generic spread of research ideas and quantify the impact of where an idea originates on its longterm diffusion across the network. We find that research from prestigious institutions spreads more quickly and completely than work of similar quality originating from less prestigious institutions. Our analyses establish the theoretical trade-offs between university prestige and the quality of ideas necessary for efficient circulation. Our results establish faculty hiring as an underlying mechanism that drives the persistent epistemic advantage observed for elite institutions, and provide a theoretical lower bound for the impact of structural inequality in shaping the spread of ideas in science.