用于重新划分选区的平衡功率图
Balanced power diagrams for redistricting
摘要：
我们提出了一种重新划分的方法，将一个地理区域分解为子区域，称为地区，使地区的人口尽可能接近，地区是紧凑和连续的。每个区都是多边形与地理区域的交点。多边形是凸的，每个多边形的平均边数小于6。多边形往往非常紧凑。每个多边形都有一个中心。中心是与多边形相关联的居民位置的质心。该算法可以被看作是一个启发式的寻找中心和平衡分配的居民到中心，以最小化的平方距离的总和居民到中心，因此可以说，该解决方案具有低分散。
英文摘要：
We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the intersection of a polygon with the geographical area. The polygons are convex and the average number of sides per polygon is less than six. The polygons tend to be quite compact. With each polygon is associated a center. The center is the centroid of the locations of the residents associated with the polygon. The algorithm can be viewed as a heuristic for finding centers and a balanced assignment of residents to centers so as to minimize the sum of squared distances of residents to centers; hence the solution can be said to have low dispersion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
