A comparison of moving objects’ trajectories in space‐time based on descriptive and qualitative interpretations is useful in many GIS‐related studies. Qualitative relationships help to answer questions such as “Do the objects meet each other?” or “Do the objects move towards or away from each other?” Questions about moving objects can be efficiently addressed using quantitative and computational techniques such as data mining of trajectory datasets but expressed in terms of qualitative relationships. It is, however, difficult to recognize these qualitative relationships when the trajectories are large and consist of many parts, where a sophisticated qualitative relationship can be formed from the aggregation of simple ones. For this reason, this study introduces two classes of trajectory relationships: initial qualitative trajectory relationships (IQTR) and combinatory qualitative trajectory relationships (CQTR). It also suggests effective algorithmic approaches to automatically retrieve them. The proposed algorithm for IQTR using min‐heap and linked‐list data structure could effectively reduce the time complexity from O(n²) to O(n log n). For CQTRs, a divide‐and‐conquer and recursive technique and a linked‐path structure again managed to reduce the time complexity from O(n²) to O(n log n). Finally, experiments on large datasets suggest the capability of the proposed methods in terms of performance and stability.

中文翻译：

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自动提取时空中两个运动物体之间复杂的定性轨迹关系

在许多与GIS相关的研究中，基于描述性和定性的解释比较时空中的移动物体的轨迹非常有用。定性关系有助于回答诸如“对象是否彼此相遇？”之类的问题。或“物体是否朝彼此靠近或远离？” 可以使用定量和计算技术（例如轨迹数据集的数据挖掘）有效地解决有关移动对象的问题，但可以用定性关系来表示。但是，当轨迹很大且由许多部分组成时，很难识别这些定性关系，而在这些部分中，简单的定性关系可以形成复杂的定性关系。因此，本研究引入了两类轨迹关系：初始定性轨迹关系（IQTR）和组合定性轨迹关系（CQTR）。它还提出了有效的算法方法来自动检索它们。提出的使用最小堆和链表数据结构的IQTR算法可以有效地减少O（n ²）至O（n  log  n）。对于CQTR，分而治之和递归技术以及链接路径结构再次设法将时间复杂度从O（n ²）降低到O（n  log  n）。最后，在大型数据集上的实验表明了所提方法在性能和稳定性方面的能力。