Enumeration of complete set of flock patterns in trajectories

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.