Optimal Political Districting by Implicit Enumeration Techniques

An algorithm is given which finds all optimal solutions, for a given set of criteria, to political redistricting problems. Using “population units” as indivisible elements, the first phase generates all feasible districts, where feasibility indicates contiguity, compactness and limited population deviation. The second phase finds that set of M feasible districts which “covers” each population unit exactly once, and minimizes the maximum deviation of any district population from the mean district population. Computational results indicate that states with 40 counties or fewer can be solved in less than 10 minutes on an IBM 7094. However, our attempt to solve a 55 county state was unsuccessful.