Geo-Graphs: An Efficient Model for Enforcing Contiguity and Hole Constraints in Planar Graph Partitioning
成果类型：
Article
署名作者：
King, Douglas M.; Jacobson, Sheldon H.; Sewell, Edward C.; Cho, Wendy K. Tam
署名单位：
University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Southern Illinois University System; Southern Illinois University Edwardsville; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1120.1083
发表日期：
2012
页码：
1213-1228
关键词：
摘要：
Political districting is an intractable problem with significant ramifications for political representation. Districts often are required to satisfy some legal constraints, but these typically are not very restrictive, allowing decision makers to influence the composition of these districts without violating relevant laws. For example, while districts must often comprise a single contiguous area, a vast collection of acceptable solutions (i.e., sets of districts) remains. Choosing the best set of districts from this collection can be treated as a (planar) graph partitioning problem. When districts must be contiguous, successfully solving this problem requires an efficient computational method for evaluating contiguity constraints; common methods for assessing contiguity can require significant computation as the problem size grows. This paper introduces the geo-graph, a new graph model that ameliorates the computational burdens associated with enforcing contiguity constraints in planar graph partitioning when each vertex corresponds to a particular region of the plane. Through planar graph duality, the geo-graph provides a scale-invariant method for enforcing contiguity constraints in local search. Furthermore, geo-graphs allow district holes (which typically are considered undesirable) to be rigorously and efficiently integrated into the partitioning process.