Abstract
Efficiently retrieving relevant data from a huge spatial database is and has been the subject of research in fields like database systems, geographic information systems and also computational geometry for many years. In this context, we study the retrieval of relevant points with respect to a query and a scoring function: let P and Q be point sets in the plane, the skyline of P with respect to Q consists of points P for which no other point of P is closer to all points of Q. A skyline of a point set P with respect to a query set Q can be seen as the most “relevant” or “desirable” subset of P with respect to Q. As the skyline of a set P can be as large as the set P itself, it is reasonable to filter the skyline using a scoring function f, only reporting the k best skyline points with respect to f.
In this paper, we consider the top-k Manhattan spatial skyline query problem for monotone scoring functions, where distances are measured in the L 1 metric. We present an algorithm that computes the top-k skyline points in near linear time in the size of P. The presented strategy improves over the direct approach of first using the state-of-the-art algorithm to compute the Manhattan spatial skyline [1] and then filtering it by the scoring function by a log(|P|) factor. The improvement has been validated in experiments that show a speedup of up to an order of magnitude.
This research was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2011-0030044).
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References
Son, W., Hwang, S.-w., Ahn, H.-K.: MSSQ: Manhattan Spatial Skyline Queries. In: Pfoser, D., Tao, Y., Mouratidis, K., Nascimento, M.A., Mokbel, M., Shekhar, S., Huang, Y. (eds.) SSTD 2011. LNCS, vol. 6849, pp. 313–329. Springer, Heidelberg (2011)
Kung, H.T., Luccio, F., Preparata, F.: On finding the maxima of a set of vectors. Journal of the Association for Computing Machinery 22(4), 469–476 (1975)
Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer-Verlag (1985)
Börzsönyi, S., Kossmann, D., Stocker, K.: The skyline operator. In: ICDE 2001: Proc. of the 17th International Conference on Data Engineering, pp. 421–430. IEEE Computer Society (2001)
Godfrey, P., Shipley, R., Gryz, J.: Maximal vector computation in large data sets. In: VLDB 2005: Proc. of the 31st International Conference on Very Large Data Bases, pp. 229–240. IEEE Computer Society (2005)
Chomicki, J., Godfery, P., Gryz, J., Liang, D.: Skyline with presorting. In: ICDE 2003: Proc. of the 19th International Conference on Data Engineering, pp. 717–816. IEEE Computer Society (2003)
Papadias, D., Tao, Y., Fu, G., Seeger, B.: An optimal and progressive algorithm for skyline queries. In: SIGMOD 2003: Proc. of the 2003 ACM SIGMOD International Conference on Management of Data, pp. 467–478. ACM (2003)
Sharifzadeh, M., Shahabi, C.: The spatial skyline queries. In: VLDB 2006: Proc. of the 32nd International Conference on Very Large Data Bases, pp. 751–762, VLDB Endowment (2006)
Lee, M.W., Son, W., Ahn, H.K., Hwang, S.W.: Spatial skyline queries: exact and approximation algorithms. GeoInformatica 15(4), 665–697 (2011)
Goncalves, M., Vidal, M.-E.: Reaching the top of the skyline: An efficient indexed algorithm for top-k skyline queries. In: Bhowmick, S.S., Küng, J., Wagner, R. (eds.) DEXA 2009. LNCS, vol. 5690, pp. 471–485. Springer, Heidelberg (2009)
Xu, C., Gao, Y.: A novel approach for selecting the top skyline under users’ references. In: ICIME 2010: Proc. of the 2nd IEEE International Conference on Information Management and Engineering, pp. 708–712. IEEE (2010)
Vlachou, A., Vazirgiannis, M.: Ranking the sky: Discovering the importance of skyline points through subspace dominance relationships. Data & Knowledge Engineering 69(9), 943–964 (2010)
Lee, J., You, G.W., Hwang, S.W.: Personalized top-k skyline queries in high-dimensional space. Information Systems 34(1), 45–61 (2009)
Brando, C., Goncalves, M., González, V.: Evaluating top-k skyline queries over relational databases. In: Wagner, R., Revell, N., Pernul, G. (eds.) DEXA 2007. LNCS, vol. 4653, pp. 254–263. Springer, Heidelberg (2007)
Goncalves, M., Vidal, M.-E.: Top-k skyline: A unified approach. In: Meersman, R., Tari, Z. (eds.) OTM-WS 2005. LNCS, vol. 3762, pp. 790–799. Springer, Heidelberg (2005)
Chan, T.M., Pǎtraşcu, M.: Counting inversions, offline orthogonal range counting, and related problems. In: SODA 2010: Proc. of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 161–173. Society for Industrial and Applied Mathematics (2010)
Rockafellar, R.T.: Convex Analysis. Princeton University Press (1996)
Blelloch, G.E.: Space-efficient dynamic orthogonal point location, segment intersection, and range reporting. In: SODA 2008: Proc. of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 894–903. Society for Industrial and Applied Mathematics (2008)
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Son, W., Stehn, F., Knauer, C., Ahn, HK. (2014). Top-k Manhattan Spatial Skyline Queries. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_5
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DOI: https://doi.org/10.1007/978-3-319-04657-0_5
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