On the Complexity of Sampling Redistricting Plans

June 10, 2022 Β· Declared Dead Β· πŸ› arXiv.org

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Authors Moses Charikar, Paul Liu, Tianyu Liu, Thuy-Duong Vuong arXiv ID 2206.04883 Category cs.DS: Data Structures & Algorithms Cross-listed cs.CG Citations 8 Venue arXiv.org Last Checked 4 months ago
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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