Efficient order-sensitive activity trajectory search

In this paper, we study the problem of order-sensitive activity trajectory search. Given a query containing a set of time-order target locations, the problem is to find the most suitable trajectory from the trajectory database such that the resulting trajectory can achieve the minimum distance from the query. We formulate the problem using two different order-sensitive distance functions: the sum-up objective function, and the maximum objective function. For the sum-up objective function, we propose a dynamic programming (DP) algorithm with time complexity O(mn²) where m is the length of the trajectory and n is the number of query locations. To improve the efficiency, we also propose an improved DP algorithm. For the maximum objective function, we propose exact and approximation algorithms to tackle it. The approximation algorithm achieves a near-optimal performance ratio, and it improves the time complexity from O(mn²) to O(n\log (d/\epsilon)) in comparison with the DP algorithm. Extensive experimental studies over both synthetic and real-world datasets demonstrate the efficiency and effectiveness of our approaches.