Rapid Detection of the Smallest k-Minimum Bounding Rectangles for Moving Objects

초록

Detecting dense regions in spatial datasets is essen-tial for many applications, including computer vision and geo-graphic information systems. Identifying the smallest k-minimum bounding rectangle (k-MBR), the smallest axis-parallel rectangle enclosing k points, is an option to detect dense regions. The complexity of this task is further amplified with the emergence of moving object data generated by GPS-enabled devices and sensor networks. This paper focuses on efficiently computing and updating the smallest k-minimum bounding rectangle (k-MBR) in the presence of moving objects. To achieve this, we propose a divide and conquer algorithm with a hierar-chical cache to address the challenges of rapid computation and efficient updates. While the divide and conquer approach can efficiently calculate the smallest k- MBR given data points, our hierarchical cache enables us to save time by only re-calculating the smallest k-MBR in the region where object moving occurs. We also introduce a dynamic programming algorithm to optimize the caching plan, minimizing computational costs. Furthermore, in contrast to existing works which prove their performance solely through theoretical time complexity analysis without code implementation, we verify performance through empirical demonstrations. Extensive experiments with synthetic and real-life datasets validate the effectiveness of our approach. Our algorithm outperforms existing methods, delivering faster computation and efficient updates for computing the smallest k-MBRs. Moreover, we empirically demonstrate that our approach with caching is significantly practical even within a large-scale environment. © 2025 IEEE.

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