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On reverse-k-nearest-neighbor joins

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Abstract

A reverse k-nearest neighbour (RkNN) query determines the objects from a database that have the query as one of their k-nearest neighbors. Processing such a query has received plenty of attention in research. However, the effect of running multiple RkNN queries at once (join) or within a short time interval (bulk/group query) has only received little attention so far. In this paper, we analyze different types of RkNN joins and provide a classification of existing RkNN join algorithms. We discuss possible solutions for solving the non-trivial variants of the problem in vector spaces, including self and mutual pruning strategies. Further, we generalize the developed algorithms to general metric spaces. During an extensive performance analysis we provide evaluation results showing the IO and CPU performance of the compared algorithms for a wide range of different setups and suggest appropriate query algorithms for specific scenarios.

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Notes

  1. The check, whether the new domination count of \({e_{j}^{S}}\) exceeds k will be performed in Line 21 of Algorithm 1

  2. Each point will have itself in its kNN set, thus we need a k+1NN-join to find the kNNs of each point in S.

  3. http://www.vision.caltech.edu/Image_Datasets/Caltech256/

  4. www.rtreeportal.org/

References

  1. Bernecker T, Emrich T, Kriegel H-P, Mamoulis N, Renz M, Zhang S, Züfle A (2011) Inverse queries for multidimensional spaces. In: Proc. SSTD, pp 330–347

  2. Jarvis RA, Patrick EA (1973) Clustering using a similarity measure based on shared near neighbors. IEEETC C-22(11):1025–1034

    Google Scholar 

  3. Ankerst M, Breunig MM, Kriegel H-P, Sander J (1999) OPTICS: ordering points to identify the clustering structure. In: Proc. SIGMOD, pp 49–60

  4. Hautamäki V, Kärkkäinen I, Fränti P (2004) Outlier detection using k-nearest neighbor graph. In: Proc. ICPR, pp 430–433

  5. Jin W, Tung AKH, Han J, Wang W (2006) Ranking outliers using symmetric neighborhood relationship. In: Proc. PAKDD, pp 577–593

  6. Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proc. KDD

  7. Korn F, Muthukrishnan S (2000) Influenced sets based on reverse nearest neighbor queries. In: Proc. SIGMOD, pp 201–212

  8. Yang C, Lin K-I (2001) An index structure for efficient reverse nearest neighbor queries. In: Proc. ICDE, pp 485–492

  9. Achtert E, Böhm C, Kröger P, Kunath P, Pryakhin A, Renz M (2006) Efficient reverse k-nearest neighbor search in arbitrary metric spaces. In: Proc. SIGMOD, pp 515–526

  10. Stanoi I, Agrawal D, Abbadi AE (2000) Reverse nearest neighbor queries for dynamic databases. In: Proc. DMKD, pp 44–53

  11. Singh A, Ferhatosmanoglu H, Tosun AS (2003) High dimensional reverse nearest neighbor queries. In: Proc. CIKM, pp 91–98

  12. Tao Y, Papadias D, Lian X (2004) Reverse kNN search in arbitrary dimensionality. In: Proc. VLDB, pp 744–755

  13. Emrich T, Kriegel H-P, Kröger P, Niedermayer J, Renz M, Züfle A (2013) A mutual-pruning approach for rknn join processing. In: Proc. BTW, pp 21–35

  14. Emrich T, Kriegel H-P, Kröger P, Niedermayer J, Renz M, Züfle A (2013) Reverse-k-nearest-neighbor join processing. In: Proc. SSTD, pp 277–294

  15. Wu W, Yang F, Chan C-Y, Tan K (2008) FINCH: evaluating reverse k-nearest-neighbor queries on location data. In: Proc. VLDB, pp 1056–1067

  16. Böhm C, Krebs F (2004) The k-nearest neighbor join: turbo charging the KDD process. KAIS 6(6):728–749

    Google Scholar 

  17. Zhang J, Mamoulis N, Papadias D, Tao Y (2004) All-nearest-neighbors queries in spatial databases. In: Proc. SSDBM, pp 297–306

  18. Yu C, Zhang R, Huang Y, Xiong H (2010) High-dimensional knn joins with incremental updates. Geoinformatica 14(1):55–82

    Article  Google Scholar 

  19. Venkateswaran JG (2007) Indexing techniques for metric databases with costly searches, Ph.D. dissertation, University of Florida, Gainesville, FL, USA, aAI3300799

  20. Tao Y, Yiu ML, Mamoulis N (2006) Reverse nearest neighbor search in metric spaces. IEEE TKDE 18(9):1239–1252

    Google Scholar 

  21. Cheema MA, Lin X, Zhang W, Zhang Y (2011) Influence zone: efficiently processing reverse k nearest neighbors queries. In: ICDE, pp 577–588

  22. Achtert E, Kriegel H-P, Kröger P, Renz M, Züfle A (2009) Reverse k-nearest neighbor search in dynamic and general metric databases. In: Proc. EDBT, pp 886–897

  23. Kriegel H-P, Kröger P, Renz M, Züfle A, Katzdobler A (2009) Reverse k-nearest neighbor search based on aggregate point access methods. In: Proc. SSDBM, pp 444–460

  24. Xia C, Hsu W, Lee ML (2005) ERkNN: efficient reverse k-nearest neighbors retrieval with local kNN-distance estimation. In: Proc. CIKM, pp 533–540

  25. Papadias D, Kalnis P, Zhang J, Tao Y (2001) Efficient olap operations in spatial data warehouses. In: Proc. SSTD, pp 443–459

  26. Kriegel H-P, Kröger P, Renz M, Züfle A, Katzdobler A (2009) Incremental reverse nearest neighbor ranking. In: Proc. ICDE, pp 1560–1567

  27. Emrich T, Kriegel H-P, Kröger P, Renz M, Züfle A (2010) Boosting spatial pruning: on optimal pruning of mbrs. In: Proc. SIGMOD, pp 39–50

  28. Achtert E, Hettab A, Kriegel H-P, Schubert E, Zimek A (2011) Spatial outlier detection: data, algorithms, visualizations. In: Proc. SSTD, pp 512–516

  29. Ciaccia P, Patella M, Zezula P (1997) M-Tree: an efficient access method for similarity search in metric spaces. In: Proc. VLDB, pp 426–435

  30. Emrich T (2013) Coping with distance and location dependencies in spatial, temporal and uncertain data, Ph.D. dissertation, Ludwig-Maximilians University Munich

  31. Emrich T, Graf F, Kriegel H-P, Schubert M, Thoma M (2010) On the impact of flash ssds on spatial indexing. In: Proc. DaMoN, pp 3–8

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Authors and Affiliations

  1. Institute for Informatics, Ludwig-Maximilians-Universität München, München, Germany

    Tobias Emrich, Hans-Peter Kriegel, Peer Kröger, Johannes Niedermayer, Matthias Renz & Andreas Züfle

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  1. Tobias Emrich
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  2. Hans-Peter Kriegel
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  3. Peer Kröger
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  4. Johannes Niedermayer
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  5. Matthias Renz
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  6. Andreas Züfle
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Correspondence to Johannes Niedermayer.

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Emrich, T., Kriegel, HP., Kröger, P. et al. On reverse-k-nearest-neighbor joins. Geoinformatica 19, 299–330 (2015). https://doi.org/10.1007/s10707-014-0215-5

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  • DOI: https://doi.org/10.1007/s10707-014-0215-5

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