We optimize pipeline parallelism for deep neural network (DNN) inference by partitioning model graphs into $k$ stages and minimizing the running time of the bottleneck stage, including communication. We design practical algorithms for this NP-hard problem and show that they are nearly optimal in practice by comparing against strong lower bounds obtained via novel mixed-integer programming (MIP) formulations. We apply these algorithms and lower-bound methods to production models to achieve substantially improved approximation guarantees compared to standard combinatorial lower bounds. For example, evaluated via geometric means across production data with $k=16$ pipeline stages, our MIP formulations more than double the lower bounds, improving the approximation ratio from $2.175$ to $1.058$. This work shows that while max-throughput partitioning is theoretically hard, we have a handle on the algorithmic side of the problem in practice and much of the remaining challenge is in developing more accurate cost models to feed into the partitioning algorithms.

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