生成树与选区重划：采样与验证的新方法
Spanning Trees and Redistricting: New Methods for Sampling and Validation
AI总结：
针对选区重划中的格里蝾螈识别问题，本文提出可逆重组算法与适配的生成树分布规范采样方法，结合高效开源实现，提供了迄今最强的不公平划分检测零模型。
摘要：
判断某一政治选区划分方案是否被隐藏议程扭曲，或是是否稀释了某一群体的投票权，需要中立的比较基准。值得注意的是，目前美国最高法院全部九位大法官均已签署相关裁决，认定计算方法可提供关键证据。当前，选区划分方案基准测试的主流方法基于生成树来对图分区进行采样。本文提出一种全新的可逆重组（reversible recombination）算法，并严格证明了其基础性质。此外，本文提出一种名为生成树分布（spanning tree distribution）的规范采样分布，该分布非常适配选区重划场景，为不同方法的比较与验证提供了严谨的理论基础。结合可生成并处理大规模数据集的高效开源实现，本研究为格里蝾螈（不公平选区划分）问题提供了迄今最强的零模型，以可靠的科学方法应对紧迫的民主挑战。
英文摘要：
Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now signed on to decisions that find that computational methods can provide key evidence. Today, the leading approaches for benchmarking districting plans are based on the use of spanning trees for sampling graph partitions. We present a new *reversible recombination* algorithm and rigorously prove its fundamental properties. Furthermore, we argue for a canonical sampling distribution called the *spanning tree distribution* that is well adapted to redistricting and provides a principled foundation for comparing and validating methods. Together with a highly efficient (and open-source) implementation that can generate and handle large datasets, this work provides the most powerful null model to date for the gerrymandering problem, meeting an urgent democratic challenge with sound scientific methodology.
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