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Geo-Graphs: An Efficient Model for Enforcing Contiguity and Hole Constraints in Planar Graph Partitioning

Author

Listed:
  • Douglas M. King

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, Illinois 61801)

  • Sheldon H. Jacobson

    (Department of Computer Science, University of Illinois, Urbana, Illinois 61801)

  • Edward C. Sewell

    (Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois 62026)

  • Wendy K. Tam Cho

    (Department of Political Science and Statistics, National Center for Supercomputing Applications, University of Illinois, Urbana, Illinois 61801)

Abstract

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.

Suggested Citation

  • Douglas M. King & Sheldon H. Jacobson & Edward C. Sewell & Wendy K. Tam Cho, 2012. "Geo-Graphs: An Efficient Model for Enforcing Contiguity and Hole Constraints in Planar Graph Partitioning," Operations Research, INFORMS, vol. 60(5), pages 1213-1228, October.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1213-1228
    DOI: 10.1287/opre.1120.1083
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    References listed on IDEAS

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    1. W. Macmillan, 2001. "Redistricting in a GIS environment: An optimisation algorithm using switching-points," Journal of Geographical Systems, Springer, vol. 3(2), pages 167-180, August.
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    3. Ricca, Federica & Simeone, Bruno, 2008. "Local search algorithms for political districting," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1409-1426, September.
    4. Burcin Bozkaya & Erhan Erkut & Dan Haight & Gilbert Laporte, 2011. "Designing New Electoral Districts for the City of Edmonton," Interfaces, INFORMS, vol. 41(6), pages 534-547, December.
    5. Bozkaya, Burcin & Erkut, Erhan & Laporte, Gilbert, 2003. "A tabu search heuristic and adaptive memory procedure for political districting," European Journal of Operational Research, Elsevier, vol. 144(1), pages 12-26, January.
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    Cited by:

    1. Camacho-Collados, M. & Liberatore, F. & Angulo, J.M., 2015. "A multi-criteria Police Districting Problem for the efficient and effective design of patrol sector," European Journal of Operational Research, Elsevier, vol. 246(2), pages 674-684.
    2. Vangerven, Bart & Briskorn, Dirk & Goossens, Dries R. & Spieksma, Frits C.R., 2022. "Parliament seating assignment problems," European Journal of Operational Research, Elsevier, vol. 296(3), pages 914-926.
    3. D. M. King & S. H. Jacobson & E. C. Sewell, 2018. "The geo-graph in practice: creating United States Congressional Districts from census blocks," Computational Optimization and Applications, Springer, vol. 69(1), pages 25-49, January.
    4. Haase, Knut & Müller, Sven, 2014. "Upper and lower bounds for the sales force deployment problem with explicit contiguity constraints," European Journal of Operational Research, Elsevier, vol. 237(2), pages 677-689.
    5. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    6. Han, Jialin & Hu, Yaoguang & Mao, Mingsong & Wan, Shuping, 2020. "A multi-objective districting problem applied to agricultural machinery maintenance service network," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1120-1130.

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