When partitioning a state into political districts, a common criterion is that political subdivisions like counties should not be split across multiple districts. This criterion is encoded into most state constitutions and is sometimes enforced quite strictly by the courts. However, map drawers, courts, and the public typically do not know what amount of splitting is truly necessary, even to satisfy basic criteria like contiguity and population balance. In this paper, we provide answers for all congressional, state senate, and state house districts in the USA using 2020 census data. Our approach is based on integer programming. The associated codes and experimental results are publicly available on GitHub.
Revision submitted to Operations Research, July 2023