Contiguity-Based Optimization Models for Political Redistricting Problems

Politicalredistrictingisaprocessusedtoredrawpoliticalboundariesbasedonanumberofcriteria thatincludepopulationequality,minorityrepresentation,contiguity,andcompactness.Redistricting planscanbedifficulttodrawmanuallyandsincethe1970stheuseofcomputersinthecreationof redistrictingplanshasincreaseddramatically.Thepurposeofthispaperistoformulatetheproblemof findingredistrictingplansasoptimizationproblemsonthebasisofpopulationequalityandcontiguity. Theauthorsspecificallyaddresstheproblemfromthecontiguityperspective.Theydevelopedtwo exactoptimalmodels:onebasedonaminimumspanningtreeandonebasedonnetworkflows.They discussthespatialrepresentationandtheformulationofcontiguityforbothmodelsandcompare theperformanceofthesetwomodels,alongwithathirdmodeldevelopedintheliterature,usinga varietyofsyntheticandrealdata.Theauthors’resultsconfirmthatsuchaproblemiscomputationally intensive and more efficient methods are needed for large size problems, but with appropriate formulationapproachestheycanobtainusefulbaselinesolutionstotheseproblemswithrelatively smallsize.Theyalsofindthatmultipleoptimalsolutionswithdifferentspatialconfigurationsmay existforthesameproblem,whichpresentsanewchallengetothedevelopmentofsolutionmethods forpoliticalredistrictingproblems. KeywORdS Land Acquisition Problems, Political Redistricting Problems, Spatial Contiguity, Spatial Optimization, Strict Equal Population