Xiaoliang Geng, Takuya Takagi, Hiroki Arimura, T. Uno
In this paper, we consider the problem of mining the complete set of spatio-temporal patterns, called maximal-duration flock patterns (Gudmundsson and van Kreveld, Proc. ACM GIS 2006) from massive mobile GPS location streams. Such algorithms are useful for mining and analysis of real-time geographic streams in geographic information systems. Although a polynomial time algorithm exists for finding a maximal-duration flock pattern from a collection of trajectories, it has not been known whether it is possible to find all maximal-duration flock patterns with theoretical guarantee of its computational complexity. For this problem, we present efficient depth-first algorithms for finding all maximal-duration patterns in a collection of trajectories without duplicates that run in polynomial time per discovered pattern using polynomial space in the total size of input trajectories. To achieve the output-sensitive complexity above, our algorithms adopt depth-first search strategy to avoid the use of exponentially large memory. We also propose a speed-up technique using geometric indexes. Finally, we show experimental results on artificial data to evaluate the proposed algorithms.
在本文中，我们考虑了从大量移动GPS位置流中挖掘完整的时空模式集的问题，称为最大持续时间群模式(Gudmundsson和van Kreveld, Proc. ACM GIS 2006)。这些算法对于地理信息系统中实时地理流的挖掘和分析是有用的。虽然存在从轨迹集合中寻找最大持续时间群模式的多项式时间算法，但是否有可能在理论保证其计算复杂度的情况下找到所有最大持续时间群模式尚不清楚。对于这个问题，我们提出了有效的深度优先算法，用于在轨迹集合中找到所有最大持续时间的模式，这些模式没有重复，每个发现的模式在输入轨迹的总大小中使用多项式空间以多项式时间运行。为了实现上述输出敏感的复杂性，我们的算法采用深度优先搜索策略，以避免使用指数级大的内存。我们还提出了一种使用几何指数的加速技术。最后，我们给出了人工数据的实验结果来评估所提出的算法。
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Mark McKenney, R. Frye, Zachary Benchley, Logan Maughan
A temporal coverage operation computes the duration that a moving object covers a spatial area. We extend this notion into temporal coverage aggregates, in which the spatial area covered for a maximum or minimum amount of time by a moving region, or set of moving regions, is discovered.
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