Balanced centroidal power diagrams for redistricting
Balanced centroidal power diagrams for redistricting
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用于重新划分的平衡质心功率图
DOI：
10.1145/3274895.3274979
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Young, Neal E.
中科院分区：
文献类型：
--
作者：
Cohen-Addad, Vincent;Klein, Philip N.;Young, Neal E.
We consider考虑the problem问题of politicalredistricting政治：给定一个地理区域中人们的位置（例如美国的一个州），目标是将区域分解为子区域，称为区，以便区的人口尽可能接近，并且区是“紧凑的”和“连续的，“使用大多数美国州宪法中提到的术语和/或美国最高法院的裁决。我们研究了一种方法，输出的解决方案，其中每个地区是一个凸多边形与地理区域的交集。每个多边形的平均边数小于6。多边形趋向于相当紧凑。事实上，这个解是一个质心幂图：每个多边形在R3上有一个相关的中心，使得·中心在平面上的投影ez = 0是分配给该多边形的人的位置的质心，并且·对于分配给该多边形的每个人，该多边形的中心是所有中心中最接近的。多边形是凸的，因为它们是3D Voronoi单元与平面的交点。在定义明确的意义上，该解决方案是在平面中选择中心并选择将人员分配到这些二维中心的问题的局部最优解决方案，以便最小化受分配平衡影响的平方距离之和。这种方法的实际问题是，在现实世界的重新划分中，人们的确切位置不明。相反，输入由多边形（人口普查区块）和相关的人口组成。一个真实的选区重划不能分裂人口普查区。因此，我们提出了第二阶段，稍微扰动的解决方案，使其不分裂人口普查块。在我们的实验中，第二阶段实现了这一点，同时保持了完美的种群平衡。在精细比例下，地区多边形不再是凸形，因为它们的边界必须遵循人口普查区块的边界，但在粗略比例下，它们保留了原始多边形的形状。
We consider the problem of politicalredistricting: given the locations of people in a geographical area (e.g. a US state), the goal is to decompose the area into subareas, calleddistricts, so that the populations of the districts are as close as possible and the districts are "compact" and "contiguous," to use the terms referred to in most US state constitutions and/or US Supreme Court rulings.We study a method that outputs a solution in which each district is the intersection of a convex polygon with the geographical area. The average number of sides per polygon is less than six. The polygons tend to be quite compact. Every two districts differ in population by at most one (so we call the solutionbalanced).In fact, the solution is acentroidal power diagram: each polygon has an associatedcenterin R3such that• the projection of the center onto the planez= 0 is the centroid of the locations of people assigned to the polygon, and• for each person assigned to that polygon, the polygon's center is closest among all centers. The polygons are convex because they are the intersections of 3D Voronoi cells with the plane.The solution is, in a well-defined sense, a locally optimal solution to the problem of choosing centers in the plane and choosing an assignment of people to those 2-d centers so as to minimize the sum of squared distances subject to the assignment being balanced.A practical problem with this approach is that, in real-world redistricting, exact locations of people are unknown. Instead, the input consists of polygons (census blocks) and associated populations. A real redistricting must not split census blocks. We therefore propose asecond phasethat perturbs the solution slightly so it does not split census blocks. In our experiments, the second phase achieves this while preserving perfect population balance. The district polygons are no longer convex at the fine scale because their boundaries must follow the boundaries of census blocks, but at a coarse scale they preserve the shape of the original polygons.
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DOI：
10.1145/3139958.3140015
发表时间：
2017
期刊：
Proceedings of the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
影响因子：
--
作者：
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DOI：
10.48550/arxiv.2206.00579
发表时间：
2017
期刊：
arXiv: Applications
影响因子：
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作者：
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DOI：
10.4230/lipics.socg.2017.7
发表时间：
2019
期刊：
ArXiv
影响因子：
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作者：
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影响因子：
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作者：
P. Klein;S. Mozes
通讯作者：
S. Mozes