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SMe: explicit & implicit constrained-space probabilistic threshold range queries for moving objects

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Abstract

This paper studies the constrained-space probabilistic threshold range query (CSPTRQ) for moving objects, where objects move in a constrained-space (i.e., objects are forbidden to be located in some specific areas), and objects’ locations are uncertain. We differentiate two forms of CSPTRQs: explicit and implicit ones. Specifically, for each moving object o, we model its location uncertainty as a closed region, u, together with a probability density function. We also model a query range, R, as an arbitrary polygon. An explicit query can be reduced to a search (over all the u) that returns a set of tuples in form of (o, p) such that p ≥ p t , where p is the probability of o being located in R, and 0≤p t ≤ 1 is a given probabilistic threshold. In contrast, an implicit query returns only a set of objects (without attaching the specific probability information), whose probabilities being located in R are higher than p t . The CSPTRQ is a variant of the traditional probabilistic threshold range query (PTRQ). As objects moving in a constrained-space are common, clearly, it can also find many applications. At the first sight, our problem can be easily tackled by extending existing methods used to answer the PTRQ. Unfortunately, those classical techniques are not well suitable for our problem, due to a set of new challenges. Another method used to answer the constrained-space probabilistic range query (CSPRQ) can be easily extended to tackle our problem, but a simple adaptation of this method is inefficient, due to its weak pruning/validating capability. To solve our problem, we develop targeted solutions that are easy-to-understand and also easy-to-implement. Our central idea is to swap the order of geometric operations and to compute the appearance probability in a multi-step manner. We demonstrate the efficiency and effectiveness of the proposed methods through extensive experiments. Meanwhile, from the experimental results, we further perceive the difference between explicit and implicit queries; this finding is interesting and also meaningful especially for the topics of other types of probabilistic threshold queries.

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Notes

  1. It is noteworthy that the traditional probabilistic range query (PRQ) usually refers to the explicit form but p t = 0, and so the immediate purposes/applications of the explicit CSPTRQ are the similar as the ones of the traditional PRQ.

  2. The traditional probabilistic threshold range query (PTRQ) usually refers to the implicit form, and so the immediate purposes/applications of the implicit CSPTRQ are similar to the ones of the traditional PTRQ.

  3. Any curve can be approximated into a polyline (e.g., by an interpolation method). Hence in theory any shaped restricted area or query range can be approximated into a polygon.

  4. If the time based update policy is assumed to be adopted, such a topic is more interesting and also more challenging, since the uncertainty region u is to be a continuously changing geometry over time. See, e.g., [39] for a clue about the relation between the location update policy and the uncertainty region u.

  5. Note that, the algorithm in [39] cannot support the generic shaped query range, and thus some modifications are necessary and inevitable when we compute u ∩ R; moreover, the details of managing complicated geometric regions (e.g., u) can be found in that paper.

  6. Note that in our implementation, we employ the map container of C++ STL (standard template library).

  7. The CA is available in site: http://www.cs.utah.edu/lifeifei/SpatialDataset.htm, and the LB is available in site: http://www.rtreeportal.org/.

  8. More information can be obtained in site: http://dev.mysql.com/doc/refman/5.1/en/spatial-extensions.html.

  9. Note that, the efficiency of the baseline method for the explicit and implicit queries are identical; for ease of presentation, we here do not differentiate them.

  10. The reason is that, for two groups of restricted area records with different ζ, the group of restricted area records with more edges usually occupy more disk space, which renders more time on skipping between different disk pages, when we fetch a series of MBRs from database. Further demonstration is beyond the theme of this paper.

  11. Here the improvement factor refers to the ratio of time. Assume that the I/O time of PE is 0.8736 seconds and the one of PI + O is 0.274 seconds, for example, the improvement factor is \(\frac {0.8736}{0.0.274}=3.189\).

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Acknowledgments

This work was supported by the National Basic Research 973 Program of China (No. 2015CB352403), the NSFC (No. 61202024, 61202025, 61370055, 61428204), the EU FP7 CLIMBER project (No. PIRSES-GA-2012-318939), the Scientific Innovation Act of STCSM (No. 13511504200), the RGC Project of Hongkong (No. 711110), the Natural Science Foundation of Shanghai (No. 12ZR1445000), Shanghai Educational Development Foundation Shanghai Chenguang Project (No. 12CG09), Shanghai Pujiang Program (No. 13PJ1403900), the Program for Changjiang Scholars and Innovative Research Team in University of China (IRT1158, PCSIRT), Singapore NRF (CREATE E2S2), the State High-Tech Development Plan (No. 2013AA01A601).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Scalable Computing and Systems, Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Zhi-Jie Wang, Bin Yao, Xiaofeng Gao, Haibing Guan & Minyi Guo

  2. Department of Computer Science, University of Hong Kong, Hongkong, China

    Reynold Cheng

  3. Institute of Computer Science and Technology, Peking University, Beijing, China

    Lei Zou

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  1. Zhi-Jie Wang
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  4. Xiaofeng Gao
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Correspondence to Zhi-Jie Wang or Bin Yao.

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Wang, ZJ., Yao, B., Cheng, R. et al. SMe: explicit & implicit constrained-space probabilistic threshold range queries for moving objects. Geoinformatica 20, 19–58 (2016). https://doi.org/10.1007/s10707-015-0230-1

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