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General Purpose Index-Based Method for Efficient MaxRS Query

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Database and Expert Systems Applications (DEXA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9827))

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Abstract

The Maximizing Range Sum problem is widely applied in facility locating, spatial data mining, and clustering problems. The current most efficient method solves it in time \(O(n\log n)\) for a particular given rectangle size. This is inefficient in cases where the queries are frequently called with different parameters. Thus, in this paper, we propose an index-based method that solves the maxRS query in time \(O(\log n)\) for any given query. Besides, our method can be used to solve the k-enclosing problem in time O(1) for any given k value if indexes are sorted according to the optimizing criteria, or \(O((n-k)^{2}k+n\log n)\) without using any index, which is comparative to the current most efficient work.

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Notes

  1. 1.

    W.l.o.g., we assume that no two points have the same x (or y) coordinate.

  2. 2.

    The proof is obvious and omitted due to space limitation.

  3. 3.

    R1 is dominated by R2 if both the width and height of R1 are larger than or equal to that of R2, the dominance relationship is formally defined in Definition 3.

  4. 4.

    \(L_1\) contains the only point (0, 0).

  5. 5.

    In the pseudocode of Algorithm 2 Line 12, we make the optimization by calling \(RMQ_{T_{k}}(1, |T_k|)\) rather than \(RMQ_{T_{k}}(r-k+1, l)\). We omit the proof here.

  6. 6.

    Based on the property that \( \forall q \in L_{k}\), there exists \(q' \in L_{k-1}\) such that \(q'\) dominates q.

  7. 7.

    www.rtreeportal.org.

References

  1. Imai, H., Asano, T.: Finding the connected components and a maximum clique of an intersection graph of rectangles in the plane. J. Algorithms 4(4), 310–323 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  2. Nandy, S.C., Bhattacharya, B.B.: A unified algorithm for finding maximum and minimum object enclosing rectangles and cuboids. Math. Appl. 29(8), 45–61 (1995)

    MathSciNet  MATH  Google Scholar 

  3. Choi, D.W., Chung, C.W., Tao, Y.: A scalable algorithm for maximizing range sum in spatial databases. Proc. VLDB Endow. 5(11), 1088–1099 (2012)

    Article  Google Scholar 

  4. Tao, Y., Hu, X., Choi, D.W., Chung, C.W.: Approximate MaxRS in spatial databases. PVLDB 6(13), 1546–1557 (2013)

    Google Scholar 

  5. Choi, D.W., Chung, C.W., Tao, Y.: Maximizing range sum in external memory. ACM Trans. Database Syst. 39(3), 21:1–21:44 (2014)

    Article  MathSciNet  Google Scholar 

  6. Das, A.S., Gupta, P., Srinathan, K., Kothapalli, K.: Finding maximum density axes parallel regions for weighted point sets. In: CCCG (2011)

    Google Scholar 

  7. Goodrich, M.T., Tsay, J.-J., Vengroff, D.E., Vitter, J.S.: External-memory computational geometry (preliminary version). In: FOCS, pp. 714–723 (1993)

    Google Scholar 

  8. Aggarwal, A., Imai, H., Katoh, N., Suri, S.: Finding k points with minimum diameter and related problems. J. Algorithms 12, 38–56 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. Datta, A., Lenhof, H.E., Schwarz, C., Smid, M.: Static and dynamic algorithms for k-point clustering problems. J. Algorithms 19, 474–503 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Eppstein, D., Erickson, J.: Iterated nearest neighbors and finding minimal polytopes. Discrete Comput. Geom. 11, 321–350 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  11. Segal, M., Kedem, K.: Enclosing k points in the smallest axis parallel rectangle. Inf. Process. Lett. 65, 95–99 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Matouek, J.: On geometric optimization with few violated constraints. Discrete Comput. Geom. 14, 365–384 (1995)

    Article  MathSciNet  Google Scholar 

  13. Hartigan, J.A.: Clustering Algorithms. Wiley, New York (1975)

    MATH  Google Scholar 

  14. Abellanas, M., Hurtado, F., Icking, C., Klein, R., Langetepe, E., Ma, L., Palop, B., Sacristán, V.: Smallest color-spanning objects. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 278–289. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Efrat, A., Sharir, M., Ziv, A.: Computing the smallest k-enclosing circle and related problems. Comput. Geom. Theory App. 4(3), 119–136 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mahapatra, P.R.S., Karmakar, A., Das, S., Goswami, P.P.: k-enclosing axis-parallel square. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part III. LNCS, vol. 6784, pp. 84–93. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Das, S., Goswami, P.P., Nandy, S.C.: Smallest k-point enclosing rectangle and square of arbitrary orientation. Inf. Process. Lett. 94, 259–266 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Mukherjee, M., Chakraborty, K.: A polynomial time optimization algorithm for a rectilinear partitioning problem with applications in VLSI design automation. Inf. Process. Lett. 83, 41–48 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Tiwari, S., Kaushik, H.: Extracting region of interest (ROI) details using LBS infrastructure and web databases. In: MDM 2012, pp. 376–379 (2012)

    Google Scholar 

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Acknowledgements

This work was partially done when X. Zhou and W. Wang visited Hong Kong Baptist University. W. Wang was supported by ARC DP 130103401 and 130103405. J. Xu was supported by HK-RGC grants 12201615 and HKBU12202414.

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Authors and Affiliations

  1. University of New South Wales, Sydney, Australia

    Xiaoling Zhou & Wei Wang

  2. Hong Kong Baptist University, Hong Kong, China

    Jianliang Xu

Authors
  1. Xiaoling Zhou
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  2. Wei Wang
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Correspondence to Xiaoling Zhou .

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Editors and Affiliations

  1. Clausthal University of Technology , Clausthal-Zellerfeld, Germany

    Sven Hartmann

  2. Victoria University of Wellington , Wellington, New Zealand

    Hui Ma

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Zhou, X., Wang, W., Xu, J. (2016). General Purpose Index-Based Method for Efficient MaxRS Query. In: Hartmann, S., Ma, H. (eds) Database and Expert Systems Applications. DEXA 2016. Lecture Notes in Computer Science(), vol 9827. Springer, Cham. https://doi.org/10.1007/978-3-319-44403-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-44403-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44402-4

  • Online ISBN: 978-3-319-44403-1

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