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首页> 外文会议>ICCSA 2011;International conference on computational science and its applications >Optimizing the Layout of Proportional Symbol Maps
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Optimizing the Layout of Proportional Symbol Maps

机译：优化比例符号图的布局

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摘要

Proportional symbol maps are a cartographic tool to assist in the visualization and analysis of quantitative data associated with specific locations (earthquake magnitudes, oil well production, temperature at weather stations, etc.). Symbol sizes are proportional to the magnitude of the quantities that they represent. We present a novel integer programming model to draw opaque disks on a map with the objective of maximizing the total visible border of all disks (an established measure of quality). We focus on drawings obtained by layering symbols on top of each other, known as stacking drawings. We introduce decomposition techniques, and several new families of facet-defining inequalities, which are implemented in a cut-and-branch algorithm. We assess the effectiveness of our approach through a series of computational experiments using real demographic and geophysical data. To the best of our knowledge, we are the first to provide provably optimal solutions to some of those problem instances.
机译：比例符号图是一种制图工具，有助于可视化和分析与特定位置（地震震级，油井产量，气象站温度等）相关的定量数据。符号大小与它们表示的数量的大小成正比。我们提出了一种新颖的整数编程模型，可以在地图上绘制不透明磁盘，以最大化所有磁盘的总可见边界（已建立的质量度量）为目标。我们专注于通过将符号彼此层叠而获得的图形，称为堆叠图形。我们介绍了分解技术，以及在分枝算法中实现的几个新的方面定义不等式系列。我们通过一系列使用实际人口统计和地球物理数据的计算实验来评估我们方法的有效性。据我们所知，我们是第一个为某些问题实例提供可证明的最佳解决方案的公司。

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