Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We believe that low density graphs have the potential to be a useful graph class for road networks, but until now, its usefulness is limited by a lack of available tools. In this paper, we develop two fundamental tools for low density graphs, that is, a well-separated pair decomposition and an approximate distance oracle. We believe that by expanding the algorithmic toolbox for low density graphs, we can help provide a useful and realistic graph class for road networks, which in turn, may help explain the many efficient and practical heuristics available for road networks.

翻译：低密度图被视为建模道路网络的一种现实图类。相较于其他常用于道路网络的图类（如平面图、有界高速公路维度图和生成子图），低密度图具有优势。我们相信低密度图有潜力成为道路网络的有用图类，但迄今为止，其应用因缺乏可用工具而受限。本文为低密度图开发了两种基础工具：一种良好分离对分解和一种近似距离预言机。我们相信，通过扩展低密度图的算法工具箱，能够为道路网络提供一个实用且现实的图类，进而有助于解释现有众多针对道路网络的高效实用启发式算法。