Focusing on Stable Roommates (SR) instances, we contribute to the toolbox for conducting experiments for stable matching problems. We introduce a polynomial-time computable pseudometric to measure the similarity of SR instances, analyze its properties, and use it to create a map of SR instances. This map visualizes 460 synthetic SR instances (each sampled from one of ten different statistical cultures) as follows: Each instance is a point in the plane, and two points are close on the map if the corresponding SR instances are similar to each other. Subsequently, we conduct several exemplary experiments and depict their results on the map, illustrating the map's usefulness as a non-aggregate visualization tool, the diversity of our generated dataset, and the need to use instances sampled from different statistical cultures. Lastly, to demonstrate that our framework can also be used for other matching problems under preference, we create and analyze a map of Stable Marriage instances.
翻译:以稳定室友为焦点, 我们为进行稳定匹配问题实验的工具箱贡献了力量。 我们引入了多米时可比较的伪计, 以测量SR实例的相似性, 分析其属性, 并用它来绘制SR实例的地图。 这个地图将460个合成SR实例( 从10种不同统计文化中的一种中抽取的样本 ) 呈现如下: 每个实例都是平面上的一个点, 如果相应的SR实例彼此相似, 两点都接近于地图上。 随后, 我们进行了几个示范性实验, 并在地图上描绘了它们的结果, 展示了地图作为非聚合可视化工具的实用性, 我们生成数据集的多样性, 以及使用从不同统计文化中抽样的实例的必要性 。 最后, 为了证明我们的框架也可以用于其他相匹配的特选问题, 我们创建并分析一张表格婚姻实例的地图 。