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On the Complexity of Sampling Redistricting Plans
Published 10 Jun 2022 in cs.DS and cs.CG | (2206.04883v2)
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.
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