We develop effective methods for constructing an ensemble of district plans via independent sampling from a reasonable probability distribution on the space of graph partitions. We compare the performance of our algorithms to that of standard Markov Chain based algorithms in the context of grid graphs and state congressional and legislative maps. For the case of perfect population balance between districts, we provide an explicit description of the distribution from which our method samples.

翻译：我们开发了有效的方法，通过从图划分空间上的合理概率分布中独立采样来构建区域规划集合。我们将算法的性能与基于标准马尔可夫链的算法在网格图以及州国会与立法选举地图的背景下进行了比较。针对区域间完美人口平衡的情况，我们提供了该方法所采样分布的显式描述。