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Given a set D of trajectories, a query object q, and a query time extent C, a mutual (i.e., symmetric) nearest neighbor (MNN) query over trajectories finds from D, the set of trajectories that are among the k 1 nearest neighbors (NNs) of q within C, and meanwhile, have q as one of their k 2 NNs. This type of queries is useful in many applications such as decision making, data mining, and pattern recognition, as it considers both the proximity of the trajectories to q and the proximity of q to<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ins.2010.02.010">doi:10.1016/j.ins.2010.02.010</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rdg3hpwcbrhjpnb2x43qje6n24">fatcat:rdg3hpwcbrhjpnb2x43qje6n24</a> </span>
more »... e trajectories. In this paper, we first formalize MNN search and identify its characteristics, and then develop several algorithms for processing MNN queries efficiently. In particular, we investigate two classes of MNN queries, i.e., MNN P and MNN T queries, which are defined with respect to stationary query points and moving query trajectories, respectively. Our methods utilize the batch processing and reusing technology to reduce the I/O cost (i.e., number of node/page accesses) and CPU time significantly. In addition, we extend our techniques to tackle historical continuous MNN (HCMNN) search for moving object trajectories, which returns the mutual nearest neighbors of q (for a specified k 1 and k 2 ) at any time instance of C. Extensive experiments with real and synthetic datasets demonstrate the performance of our proposed algorithms in terms of efficiency and scalability. Ó 2010 Elsevier Inc. All rights reserved. A preliminary version of this work has been published in the Proceedings of the 9th International Conference on Mobile Data Management (MDM 2008). Substantial new technical materials have been added to this journal submission. Specifically, the paper extends the MDM 2008 paper by mainly including (i) processing of the HCMNN query with respect to stationary query points, called HCMNN P retrieval (Section 5), (ii) processing of the HCMNN query with respect to moving query trajectories, called HCMNN T search (Section 5), and (iii) enhanced experimental evaluation that incorporates the new classes of queries (Section 6). Notes: (i) This manuscript is the authors' original work and has not been published nor has it been submitted simultaneously elsewhere, except for the preliminary version (i.e.,  ) mentioned previously; (ii) The main differences between the conference version and this submission are stated above; and (iii) All authors have checked the manuscript and have agreed to the submission.
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