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Wow, this proposed approach to drawing districts without gerrymandering is fascinating! In the spirit of "I cut you choose", the proposal is "One party defines 2N equal-population sub-districts, and the other party chooses pairs of adjacent sub-districts to combine, to form N districts."
The analysis in the body of the paper focuses on simulations of each party's optimal strategy in the context of some real-world maps of US voting precincts, while an appendix proves a few theorems giving bounds in the alternate context where the pairs of districts that get combined don't need to be geographically adjacent. (If this idea catches on, I'd bet someone will produce theoretical bounds in the presence of the geography constraint.)
A Partisan Solution to Partisan Gerrymandering: The Define–Combine Procedure
@Log3overLog2 It's interesting that they don't cite a 2017 paper that claims to give a protocol that solves this exactly. The solution in the paper you cited is only approximate.
@jdchristensen That work and others are cited and contrasted in Section 2, "Limitations of Current Partisan Gerrymandering Fixes".
@Log3overLog2 Oh, you're right, they do briefly mention that paper. But they don't really say much of substance about why that solution (or others) aren't adequate.