De novo DNA synthesis is in need of new ideas for increasing production rate and reducing cost. DNA reuse in combinatorial library construction is one such idea. Here, we describe an algorithm for planning multistage assembly of DNA libraries with shared intermediates that greedily attempts to maximize DNA reuse, and show both theoretically and empirically that it runs in linear time. We compare solution quality and algorithmic performance to the best results reported for computing DNA assembly graphs, finding that our algorithm achieves solutions of equivalent quality but with dramatically shorter running times and substantially improved scalability. We also show that the related computational problem bounded-depth min-cost string production (BDMSP), which captures DNA library assembly operations with a simplified cost model, is NP-hard and APX-hard by reduction from vertex cover. The algorithm presented here provides solutions of near-minimal stages and thanks to almost instantaneous planning of DNA libraries it can be used as a metric of "manufacturability" to guide DNA library design. Rapid planning remains applicable even for DNA library sizes vastly exceeding today's biochemical assembly methods, future-proofing our method.