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arXiv · 2206.04883

On the Complexity of Sampling Redistricting Plans

Moses Charikar·Paul Liu·Tianyu Liu·Thuy-Duong Vuong
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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.

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Moses Charikar, Paul Liu, Tianyu Liu, Thuy-Duong Vuong. 2022-06-10. On the Complexity of Sampling Redistricting Plans. https://arxiv.org/abs/2206.04883

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