English

On the Complexity of Sampling Redistricting Plans

Data Structures and Algorithms 2023-10-26 v2 Computational Geometry

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 Z2.\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.

Cite

@article{arxiv.2206.04883,
  title  = {On the Complexity of Sampling Redistricting Plans},
  author = {Moses Charikar and Paul Liu and Tianyu Liu and Thuy-Duong Vuong},
  journal= {arXiv preprint arXiv:2206.04883},
  year   = {2023}
}

Comments

Correcting the definition of Markov chain to sample from spanning tree distribution

R2 v1 2026-06-24T11:46:00.390Z