Linear-size formulations for connected planar graph partitioning and political districting
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11590_2023_2070_ReferencePDF.pdf
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Author(s)
Zhang, Jack
Validi, Hamidreza
Buchanan, Austin
Hicks, Illya V.
Date Issued
October 5, 2023
Publisher
Springer Berlin Heidelberg
Citation
Zhang, Jack, Validi, Hamidreza, Buchanan, Austin and Hicks, Illya V. 2023. "Linear-size formulations for connected planar graph partitioning and political districting."
Version
Author's final manuscript
Abstract
Motivated by applications in political districting, we consider the task of partitioning the n vertices of a planar graph into k connected components. We propose an extended formulation for this task that has two desirable properties: (i) it uses just O(n) variables, constraints, and nonzeros, and (ii) it is perfect. To explore its ability to solve real-world problems, we apply it to a political districting problem in which contiguity and population balance are imposed as hard constraints and compactness is optimized. Computational experiments show that, despite the model’s small size and integrality for connected partitioning, the population balance constraints are more troublesome to effectively impose. Nevertheless, we share our findings in hopes that others may find better ways to impose them.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s11590-023-02070-0
