Cubic upper and lower bounds for subtrajectory clustering under the continuous Fréchet distance
ACM-SIAM Symposium on Discrete Algorithms (SODA)(2022)
摘要
Detecting commuting patterns or migration patterns in movement data is an important problem in computational movement analysis. Given a trajectory, or set of trajectories, this corresponds to clustering similar subtrajectories. We study subtrajectory clustering under the continuous and discrete Fréchet distances. The most relevant theoretical result is by Buchin et al. (2011). They provide, in the continuous case, an O(n5) time algorithm1 and a 3SUM-hardness lower bound, and in the discrete case, an O(n3) time algorithm. We show, in the continuous case, an O(n3 log2 n) time algorithm and a 3OV-hardness lower bound, and in the discrete case, an O(n2 log n) time algorithm and a quadratic lower bound. Our bounds are almost tight unless SETH fails.
更多查看译文
关键词
subtrajectory clustering,distance,lower bounds
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要