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Top-k spatial distance joins

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Abstract

Top-k joins have been extensively studied when numerical valued attributes are joined on an equality predicate. Other types of join attributes and predicates have received little to no attention. In this paper, we consider spatial objects that are assigned a score (e.g., a ranking). Give two collections R, S of such objects and a spatial distance threshold 𝜖, we introduce the top-k spatial distance join (k-SDJoin) to identify the k pairs of objects, which have the highest combined score (based on an aggregate function γ) among all object pairs in R × S with a spatial distance at most 𝜖. State-the-of-art methods for relational top-k joins can be adapted for k-SDJoin, but their focus is on minimizing the number of objects accessed from the inputs; however, when spatial objects are joined, the computational cost can easily become the bottleneck. In view of this, we propose a novel evaluation algorithm, which greatly reduces the computational cost, without compromising the access cost. The main idea is to access and efficiently join blocks of objects from each collection, using appropriate bounds to avoid computing the entire spatial 𝜖-distance join. As the performance of our solution heavily relies on the size of the input blocks, we devise an approach for automated block size tuning enhanced by a novel generic model for estimating the number of objects to be accessed from each input. Contrary to previous efforts, our model employs cheap-to-compute statistics and requires no prior knowledge of data distribution. Our extensive experimental analysis demonstrates the efficiency of our algorithm compared to methods based on existing literature that prioritize either the ranking or the spatial join component of k-SDJoin queries.

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Notes

  1. An exception is the work of [21] which, however, is restricted to a specific type of attributes (probabilities) and a specific aggregation function (product).

  2. Input collections R and S need not to be sorted on their scoring attribute for example, if they stem from previous query operators which produce such interesting orders.

  3. When a dataset is sorted in descending order of its scoring attribute, the lowest seen score is equivalent to the last seen score.

  4. In this paper, we define the dist function on non-leaf entries as the minimum distance between the MBR of two tree entries bounding boxes or between the MBR of a tree entry and an object, i.e., \(dist(e,e^{\prime }) = MINDIST(e,e^{\prime })\) or dist(o, e) = MINDIST(o, e), respectively.

  5. We briefly discuss the cost of automatically determining block size λ in the next section.

  6. We denote by \(r_{c_{R}}\) and \(s_{c_{S}}\) the cR and cS-th objects in the sorted inputs, respectively.

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Authors and Affiliations

  1. Department of Computer Science, The University of Hong Kong, Hong Kong, China

    Shuyao Qi

  2. Institute of Computer Science, Johannes Gutenberg University Mainz, Mainz, Germany

    Panagiotis Bouros

  3. Department of Computer Science & Engineering, University of Ioannina, Ioannina, Greece

    Nikos Mamoulis

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  1. Shuyao Qi
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  2. Panagiotis Bouros
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  3. Nikos Mamoulis
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Correspondence to Shuyao Qi.

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Qi, S., Bouros, P. & Mamoulis, N. Top-k spatial distance joins. Geoinformatica 24, 591–631 (2020). https://doi.org/10.1007/s10707-020-00393-z

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