On the Complexity of Sampling Redistricting Plans
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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 ℤ_2. We show an alternative way to sample balance, compact and contiguous redistricting plans using a "relaxed" version of ReCom and rejection sampling.
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