Browsing by Author "Carter, D"

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    METROPOLIZED FOREST RECOMBINATION FOR MONTE CARLO SAMPLING OF GRAPH PARTITIONS
    (SIAM Journal on Applied Mathematics, 2023-08-01) Autry, E; Carter, D; Herschlag, GJ; Hunter, Z; Mattingly, JC
    We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm is able to sample from a specified measure on partitions or spanning forests. Being able to sample from a specified measure is a requirement of what we consider as the gold standard in quantifying the extent to which a particular map is a gerrymander. Our proposal chain modifies the recently developed method called recombination (ReCom), which draws spanning trees on joined partitions and then randomly cuts them to repartition. We improve the computational efficiency by augmenting the statespace from partitions to spanning forests. The extra information accelerates the computation of the forward and backward proposal probabilities which are required for the Metropolis-Hastings algorithm. We demonstrate this method by sampling redistricting plans on several measures of interest and find promising convergence results on several key observables of interest. We also explore some limitations in the measures that are efficient to sample from and investigate the feasibility of using parallel tempering to extend this space of measures.
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    Metropolized Multiscale Forest Recombination for Redistricting
    (Multiscale Modeling & Simulation, 2021-01) Autry, EA; Carter, D; Herschlag, GJ; Hunter, Z; Mattingly, JC
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    Optimal Legislative County Clustering in North Carolina
    Carter, D; Hunter, Z; Teague, D; Herschlag, G; Mattingly, J
    North Carolina's constitution requires that state legislative districts should not split counties. However, counties must be split to comply with the "one person, one vote" mandate of the U.S. Supreme Court. Given that counties must be split, the North Carolina legislature and courts have provided guidelines that seek to reduce counties split across districts while also complying with the "one person, one vote" criteria. Under these guidelines, the counties are separated into clusters. The primary goal of this work is to develop, present, and publicly release an algorithm to optimally cluster counties according to the guidelines set by the court in 2015. We use this tool to investigate the optimality and uniqueness of the enacted clusters under the 2017 redistricting process. We verify that the enacted clusters are optimal, but find other optimal choices. We emphasize that the tool we provide lists \textit{all} possible optimal county clusterings. We also explore the stability of clustering under changing statewide populations and project what the county clusters may look like in the next redistricting cycle beginning in 2020/2021.