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On the Complexity of Sampling Redistricting Plans
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abstract
A crucial task in the political redistricting problem is to sample redistricting plans i.e. a partitioning of the graph of census blocks into districts. We show that Recombination [DeFord-Duchin-Solomon'21]-a popular Markov chain to sample redistricting plans-is exponentially slow mixing on simple subgraph of $\mathbb{Z}_2.$ We show an alternative way to sample balance, compact and contiguous redistricting plans using a "relaxed" version of ReCom and rejection sampling.
Forward citations
Cited by 2 Pith papers
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Census Dual Graphs: Properties and Random Graph Models
Census dual graphs are characterized as nearly planar and nearly triangulated, with perturbed-grid and Delaunay-based random models providing the closest matches among those tested.
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Sampling Tree-Weighted Partitions Without Sampling Trees
A new algorithm samples balanced tree-weighted bipartitions directly on planar graphs in expected O(n) time, bypassing spanning tree sampling and speeding up redistricting analysis.
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