Every 10 years, United States Congressional Districts must be redesigned in response to a national census. While the size of practical political districting problems is typically too large for exact optimization approaches, heuristics such as local search can help stakeholders quickly identify good (but suboptimal) plans that suit their objectives. However, enforcing a district contiguity constraint during local search can require significant computation; tools that can reduce contiguity-based computations in large practical districting problems are needed. This paper applies the geo-graph framework to the creation of United States Congressional Districts from census blocks in four states—Arizona, Massachusetts, New Mexico, and New York—and finds that (a) geo-graph contiguity assessment algorithms reduce the average number of edges visited during contiguity assessments by at least three orders of magnitude in every problem instance when compared with simple graph search, and (b) the assumptions of the geo-graph model are easily adapted to the sometimes-irregular census block geography with only superficial impact on the solution space. These results show that the geo-graph model and its associated contiguity algorithms provide a powerful constraint assessment tool to political districting stakeholders.
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The computational work was conducted with support from the Simulation and Optimization Laboratory at the University of Illinois. This research was supported in part by the National Science Foundation [IIS-0827540]. The second author was supported in part by the Air Force Office of Scientific Research [FA9550-10-1-0387, FA9550-15-1-0100]. The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air Force, the National Science Foundation, or the United States Government. This work originally appeared in the Ph.D. dissertation of the first author .
This research was supported in part by the National Science Foundation [IIS-0827540]. The second author was supported in part by the Air Force Office of Scientific Research [FA9550-10-1-0387, FA9550-15-1-0100].
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King, D.M., Jacobson, S.H. & Sewell, E.C. The geo-graph in practice: creating United States Congressional Districts from census blocks. Comput Optim Appl 69, 25–49 (2018). https://doi.org/10.1007/s10589-017-9936-3
- Planar graphs
- Graph partitioning
- Geographic districting
- Graph connectivity