Definition
Given a query point \(\mathbf{q}\) and a set \(\mathcal{D}\) of data points, a nearest neighbor (NN) query returns the data point \(\mathbf{p}\) in \(\mathcal{D}\) that minimizes the distance \(\text{DIST}(\boldsymbol{q},\boldsymbol{p})\), where the distance function \(\text{DIST}(\boldsymbol{},\boldsymbol{})\) is the L 2norm. One important variant of this query type is kNN query, which returns k data points with the minimum distances. When taking the temporal dimension into account, the k NN query result may change over a period of time due to changes in locations of the query point and/or data points. Formally, the k-nearest neighbor (k NN) query is defined as follows.
Definition 1 (k -Nearest Neighbor (k NN) Query).
Given a set \(\mathcal{D}\) of data objects and a query point \(\mathbf{q}\), the k NN query finds a set \(\mathcal{R}\) of objects such that: (i) \(\mathcal{R}\) contains k objects from \(\mathcal{D}\)...
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References
Aurenhammer F (1991) Voronoi diagrams – a survey of a fundamental geometric data structure. ACM Comput Surv 23(3):345–405
Cheng R, Kalashnikov DV, Prabhakar S (2004) Querying imprecise data in moving object environments. IEEE Trans Knowl Data Eng 16(9):1112–1127
Chow C, Mokbel MF (2007) Enabling private continuous queries for revealed user locations. In: SSTD, Boston, MA, USA, pp 258–275
Duckham M, Kulik L (2005) A formal model of obfuscation and negotiation for location privacy. In: Pervasive computing, third international conference, PERVASIVE 2005, Munich, 8–13 May 2005, Proceedings, pp 152–170
Gao Y, Zheng B, Chen G, Chen C, Li Q (2011) Continuous nearest-neighbor search in the presence of obstacles. ACM Trans Database Syst 36(2):9
Gedik B, Liu L (2004) Mobieyes: distributed processing of continuously moving queries on moving objects in a mobile system. In: EDBT, Heraklion, Crete, Greece, pp 67–87
Gruteser M, Grunwald D (2003) Anonymous usage of location-based services through spatial and temporal cloaking. In: Proceedings of the first international conference on mobile systems, applications, and services, MobiSys 2003, San Francisco, 5–8 May 2003
Hu H, Xu J, Lee DL (2005) A generic framework for monitoring continuous spatial queries over moving objects. In: SIGMOD, Baltimore, Maryland, USA, pp 479–490
Iwerks GS, Samet H, Smith KP (2006) Maintenance of k-nn and spatial join queries on continuously moving points. ACM Trans Database Syst 31(2):485–536
Li C, Gu Y, Qi J, Yu G, Zhang R, Yi W (2014) Processing moving knn queries using influential neighbor sets. PVLDB 8(2):113–124
Mouratidis K (2009) Continuous monitoring of spatial queries. In: Encyclopedia of database systems. Springer, New York, pp 479–484
Mouratidis K, Hadjieleftheriou M, Papadias D (2005a) Conceptual partitioning: an efficient method for continuous nearest neighbor monitoring. In: SIGMOD, Baltimore, Maryland, USA, pp 634–645
Mouratidis K, Papadias D, Bakiras S, Tao Y (2005b) A threshold-based algorithm for continuous monitoring of k nearest neighbors. IEEE Trans Knowl Data Eng 17(11):1451–1464
Mouratidis K, Yiu ML, Papadias D, Mamoulis N (2006) Continuous nearest neighbor monitoring in road networks. In: VLDB, Seoul, Korea, pp 43–54
Niedermayer J, Züfle A, Emrich T, Renz M, Mamoulis N, Chen L, Kriegel H (2013) Probabilistic nearest neighbor queries on uncertain moving object trajectories. PVLDB 7(3):205–216
Nutanong S, Zhang R, Tanin E, Kulik L (2010) Analysis and evaluation of v*- k nn: an efficient algorithm for moving k nn queries. VLDB J 19(3):307–332
Okabe A, Boots B, Sugihara K (1992) Spatial tessellations: concepts and applications of Voronoi diagrams. Wiley, New York
Saltenis S, Jensen CS (2002) Indexing of moving objects for location-based services. In: ICDE, San Jose, California, USA, pp 463–472
Song Z, Roussopoulos N (2001) K-nearest neighbor search for moving query point. In: SSTD, Redondo Beach, CA, USA, pp 79–96
Tao Y, Papadias D (2002) Time-parameterized queries in spatio-temporal databases. In SIGMOD, Madison, Wisconsin, USA, pp 334–345
Tao Y, Papadias D, Shen Q (2002) Continuous nearest neighbor search. In: VLDB, Hong Kong, China, pp 287–298
Tao Y, Papadias D, Sun J (2003) The tpr*-tree: an optimized spatio-temporal access method for predictive queries. In: VLDB, Berlin, Germany, pp 790–801
Xiong X, Mokbel MF, Aref WG (2005) SEA-CNN: scalable processing of continuous k-nearest neighbor queries in spatio-temporal databases. In: ICDE, Tokyo, Japan, pp 643–654
Yu X, Pu KQ, Koudas N (2005) Monitoring k-nearest neighbor queries over moving objects. In: ICDE, Tokyo, Japan, pp 631–642
Zhang J, Zhu M, Papadias D, Tao Y, Lee DL (2003) Location-based spatial queries. In: SIGMOD, San Diego, California, USA, pp 443–454
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Nutanong, S., Ali, M., Tanin, E., Mouratidis, K. (2015). Dynamic Nearest Neighbor Queries in Euclidean Space. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-23519-6_1558-1
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DOI: https://doi.org/10.1007/978-3-319-23519-6_1558-1
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