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Optimal partisan districting on planar geographies

Author

Listed:
  • Balázs Fleiner

    (Corvinus University of Budapest)

  • Balázs Nagy

    (Corvinus University of Budapest)

  • Attila Tasnádi

    (Corvinus University of Budapest)

Abstract

We show that optimal partisan districting and majority securing districting in the plane with geographical constraints are NP-complete problems. We provide a polynomial time algorithm for determining an optimal partisan districting for a simplified version of the problem. In addition, we give possible explanations for why finding an optimal partisan districting for real-life problems cannot be guaranteed.

Suggested Citation

  • Balázs Fleiner & Balázs Nagy & Attila Tasnádi, 2017. "Optimal partisan districting on planar geographies," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 879-888, December.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:4:d:10.1007_s10100-016-0454-7
    DOI: 10.1007/s10100-016-0454-7
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    References listed on IDEAS

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    1. Puppe, Clemens & Tasnádi, Attila, 2009. "Optimal redistricting under geographical constraints: Why "pack and crack" does not work," Economics Letters, Elsevier, vol. 105(1), pages 93-96, October.
    2. 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.
    3. S. W. Hess & J. B. Weaver & H. J. Siegfeldt & J. N. Whelan & P. A. Zitlau, 1965. "Nonpartisan Political Redistricting by Computer," Operations Research, INFORMS, vol. 13(6), pages 998-1006, December.
    4. Chou, Chung-I & Li, S.P., 2006. "Taming the Gerrymander—Statistical physics approach to Political Districting Problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 799-808.
    5. Attila Tasnádi, 2011. "The political districting problem: A survey," Society and Economy, Akadémiai Kiadó, Hungary, vol. 33(3), pages 543-554, December.
    6. GARFINKEL, Robert S. & NEMHAUSER, Geroge L., 1970. "Optimal political districting by implicit enumeration techniques," LIDAM Reprints CORE 54, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. R. S. Garfinkel & G. L. Nemhauser, 1970. "Optimal Political Districting by Implicit Enumeration Techniques," Management Science, INFORMS, vol. 16(8), pages 495-508, April.
    8. Ricca, Federica & Simeone, Bruno, 2008. "Local search algorithms for political districting," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1409-1426, September.
    9. Anuj Mehrotra & Ellis L. Johnson & George L. Nemhauser, 1998. "An Optimization Based Heuristic for Political Districting," Management Science, INFORMS, vol. 44(8), pages 1100-1114, August.
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    Cited by:

    1. Tibor Csendes & Csanád Imreh & József Temesi, 2017. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 739-741, December.

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