With the growing number of mobile applications, data analysis on large sets of historical moving objects trajectories becomes increasingly important. Nearest neighbor search is a fundamental problem in spatial and spatio-temporal databases. In this paper, we consider the following problem: Given a set of moving object trajectories D and a query trajectory mq , find the k nearest neighbors to mq within D for any instant of time within the lifetime of mq . We assume D is indexed in a 3D-R-tree and employ a filter-and-refine strategy. The filter step traverses the index and creates a stream of so-called units (linear pieces of a trajectory) as a superset of the units required to build the result of the query. The refinement step processes an ordered stream of units and determines the pieces of units forming the precise result. To support the filter step, for each node p of the index, in preprocessing a time-dependent coverage function C p ( t ) is computed which is the number of trajectories represented in p present at time t . Within the filter step, sophisticated data structures are used to keep track of the aggregated coverages of the nodes seen so far in the index traversal to enable pruning. Moreover, the R-tree index is built in a special way to obtain coverage functions that are effective for pruning. As a result, one obtains a highly efficient k NN algorithm for moving data and query points that outperforms the two competing algorithms by a wide margin. Implementations of the new algorithms and of the competing techniques are made available as well. Algorithms can be used in a system context including, for example, visualization and animation of results. Experiments of the paper can be easily checked or repeated, and new experiments be performed.
The VLDB Journal – Springer Journals
Published: Oct 1, 2010
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