ABSTRACT

The naïve algorithm for generating nearest-neighbour models determines the distance between every pair of nodes, resulting in quadratic running time. Such time complexity is common among spatial problems and impedes the generation of larger spatial models. In this article, an improved algorithm for the Mocnik model, an example of nearest-neighbour models, is introduced. Instead of solving $k$ nearest-neighbour problems for each node ($k$ dynamic in the sense that it varies among the nodes), the improved algorithm presented exploits the notion of locality through introducing a corresponding spatial index, resulting in a linear average-case time complexity. This makes possible to generate very large prototypical spatial networks, which can serve as testbeds to evaluate and improve spatial algorithms, in particular, with respect to the optimization of algorithms towards big geospatial data.

摘要

用于生成最近邻模型的朴素算法确定每对节点之间的距离，从而产生二次运行时间。这种时间复杂度在空间问题中很常见，并阻碍了更大空间模型的生成。本文介绍了 Mocnik 模型的改进算法，该模型是最近邻模型的一个示例。而不是解决$ķ$每个节点的最近邻问题 ($ķ$在节点之间变化的意义上是动态的），所提出的改进算法通过引入相应的空间索引来利用局部性的概念，从而产生线性平均情况时间复杂度。这使得生成非常大的原型空间网络成为可能，它可以作为评估和改进空间算法的测试平台，特别是在针对大地理空间数据的算法优化方面。