Two-level indexes have been widely used to handle trajectories of moving objects that are constrained to a network. The top-level of these indexes handles the spatial dimension, whereas the bottom level handles the temporal dimension. The latter turns out to be an instance of the interval-intersection problem, but it has been tackled by non-specialized spatial indexes. In this work, we propose the use of a compact data structure on the bottom level of these indexes. Our experimental evaluation shows that our approach is both faster and smaller than existing solutions.
Another difference with previous solutions is that our approach uncouples the network from the trajectories. This model known as Network-Matched has been successfully used @cite_10 @cite_18 , but without using compact data structures in its implementation. Our approach has the advantage that mapping trajectories to a network facilitates the finding of similar trajectories and, in consequence, it allows a better use of space.
@cite_18 @cite_10
2153482597 2751694342 2111644456 2576109540
We consider the problem of constructing street networks from geo-referenced trajectory data: Given a set of trajectories in the plane, compute a street network that represents all trajectories in the set. We present a simple and practical incremental algorithm that is based on partial matching of the trajectories to the graph. We use minimumlink paths to reduce the complexity of the reconstructed graph. We provide quality guarantees and experimental results based on both real and synthetic data. For the partial matching we introduce a new variant of partial Frechet distance. The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider the case of trajectory similarity join (TS-Join), where the objects are trajectories of vehicles moving in road networks. Thus, given two sets of trajectories and a threshold θ, the TS-Join returns all pairs of trajectories from the two sets with similarity above θ. This join targets applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide a purposeful definition of similarity. To enable efficient TS-Join processing on large sets of trajectories, we develop search space pruning techniques and take into account the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer algorithm. For each trajectory, the algorithm first finds similar trajectories. Then it merges the results to achieve a final result. The algorithm exploits an upper bound on the spatiotemporal similarity and a heuristic scheduling strategy for search space pruning. The algorithm's per-trajectory searches are independent of each other and can be performed in parallel, and the merging has constant cost. An empirical study with real data offers insight in the performance of the algorithm and demonstrates that is capable of outperforming a well-designed baseline algorithm by an order of magnitude. We propose a network flow based optimization method for data association needed for multiple object tracking. The maximum-a-posteriori (MAP) data association problem is mapped into a cost-flow network with a non-overlap constraint on trajectories. The optimal data association is found by a min-cost flow algorithm in the network. The network is augmented to include an explicit occlusion model(EOM) to track with long-term inter-object occlusions. A solution to the EOM-based network is found by an iterative approach built upon the original algorithm. Initialization and termination of trajectories and potential false observations are modeled by the formulation intrinsically. The method is efficient and does not require hypotheses pruning. Performance is compared with previous results on two public pedestrian datasets to show its improvement. Emerging vehicular trajectory data have opened up opportunities to benefit many real-world applications, e.g., frequent trajectory based navigation systems, road planning, car pooling, etc. The similarity join is a key operation to enable such applications, which finds similar trajectory pairs from two large collections of trajectories. Existing similarity metrics on trajectories rely on aligning sampling points of two trajectories. However, due to different sampling rates or different vehicular speeds, the sample points in similar trajectories may not be aligned. To address this problem, we propose a new bi-directional mapping similarity ( @math ), which allows a sample point of a trajectory to align to the closest location (which may not be a sample point) on the other trajectory, and vice versa. Since it is expensive to enumerate every two trajectories and compute their similarity, we propose Strain-Join , a signature-based trajectory similarity join framework. Strain-Join first generates signatures for each trajectory such that if two trajectories do not share common signatures, they cannot be similar. In order to utilize this property to prune dissimilar pairs, we devise several techniques to generate high-quality signatures and propose an efficient filtering algorithm to prune dissimilar pairs. For the pairs not pruned by the filtering algorithm, we propose effective verification algorithms to verify whether they are similar. Experimental results on real datasets show that our algorithm outperforms state-of-the-art techniques in terms of both effectiveness and efficiency.