Abstract
A spatial k-NN query returns k nearest points in a point dataset to a given query point. To measure the distance between two points, most of the literature focuses on the Euclidean distance or the network distance. For many applications, such as wildlife movement, it is necessary to consider the surface distance, which is computed from the shortest path along a terrain surface. In this paper, we investigate the problem of efficient surface k-NN (sk-NN) query processing. This is an important yet highly challenging problem because the underlying environment data can be very large and the computational cost of finding the shortest path on a surface can be very high. To minimize the amount of surface data to be used and the cost of surface distance computation, a multi-resolution surface distance model is proposed in this paper to take advantage of monotonic distance changes when the distances are computed at different resolution levels. Based on this innovative model, sk-NN queries can be processed efficiently by accessing and processing surface data at a just-enough resolution level within a just-enough search region. Our extensive performance evaluations using real world datasets confirm the efficiency of our proposed model.
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Chen, J., Han, Y.: Shortest paths on a polyhedron. In: 6th ACM Symp. Comput. Geometry, pp. 360–369 (1990)
Deng, K., Zhou, X.: Expansion-based algorithms for finding single pair shortest path on surface. In: Proc. of W2GIS, pp. 254–271 (2004)
Deng, K., Zhou, X., Shen, H.T., Xu, K., Lin, X.: Surface k-NN query processing. In: ICDE (2006)
Dijkstra E.W. (1959). A note on two problems in connection with graphs. Numer. Math. 1: 269–271
Garland, M.: Multiresolution modeling: survey and future opportunities. In: Eurographics, pp. 111–131 (1999)
Garland, M., Heckbert, P.S.: Surface simplification using quadric error metrics. In: 24th Int’l Conf. on Comput. Graphics and Interactive Tech. pp. 209–216 (1997)
Hjaltason G.R. and Samet H. (1999). Distance browsing in spatial databases. TODS 24(2): 265–318
Hoppe, H.: Progressive meshes. In: SIGGRAPH (1996)
Jagadish, H., Ooi, B., Tan, K.L., Yu,C., Zhang, R.: iDistance: an adaptive B+-tree based indexing method for nearest neighbour search. TODS (2005)
Jiang, B.: I/O efficiency of shortest path algorithms: an analysis. ICDE (1992)
Kanai, T., Suzuki, H.: Approximate shortest path on polyhedral surface based on selective refinement of the discrete graph and its applications. Geom. Model. Process. 241–250 (2000)
Kaneva, B., O’Rourke, J.: An implementation of Chen & Han’s shortest paths algorithm. In: Proc. of 12th Canadian Conf. on Comput. Geom. pp. 139–146 (2000)
Kapoor, S.: Efficient computation of geodesic shortest paths. In: 31st Annual ACM Symp. on Theory of Computation, pp. 770–779 (1999)
Kolahdouzan, M.R., Shahabi, C.: Voronoi-based k nearest neighbor search for spatial network databases. VLDB (2004)
Li Z. and Openshaw S. (1992). Algorithms for automated line generalization based on a natural principle of objective generalization. J. GIS 6(5): 373–389
Mitchell, J.S.B.: Geometric shortest paths and network optimization. In: Handbook of Computational Geometry, Sack, J.-R., Urrutia, J. (eds) pp. 633–701 (2000)
Papadias, D., Zhang, J., Mamoulis, N., Tao, Y.: Query processing in spatial network databases. VLDB (2003)
Roussopoulos, N., Kelley, S., Vincent, F.: Nearest neighbor queries. SIGMOD (1995)
Seidl, T., Kriegel, H.P.: Optimal multi-step k-nearest neighbor search. SIGMOD (1998)
Shahabi, C., Kolahdouzan, M.R., Sharifzadeh, M.: A road network embedding technique for k-nearest neighbor search in moving object databases. In: ACM GIS, pp. 94–100 (2002)
Shekhar, S., Kohli, A., Coyle, M.: Path computation algorithms for advanced traveler information system (atis). ICDE (1993)
Shekhar S. and Liu D. (1997). A connectivity-cluster access method for networks and network computations. TKDE 19(1): 102–119
Tompkins, P., Stentz, T., Whittaker, W.: Mission planning for the sun-synchronous navigation field experiment. In: IEEE Int’l Conf. on Robotics and Automation, pp. 3493–3500 (2002)
Varadarajan, K.R., Agarwal, P.: Approximating shortest paths on an nonconvex polyhedron. In: Proc. 38th Annu. IEEE Symp. Found. Comput. Sci. pp. 182–191 (1997)
Weber, R., Schek, H.J., Blott, S.: A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces. VLDB (1998)
Xu, K., Zhou, X., Lin, X.: Direct mesh: a multiresolution approach to terrain visualisation. ICDE (2004)
Yiu M.L., Mamoulis N. and Papadias D. (2005). Aggregate nearest neighbor queries in road networks. TKDE 17(6): 820–833
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Deng, K., Zhou, X., Shen, H.T. et al. A multi-resolution surface distance model for k-NN query processing. The VLDB Journal 17, 1101–1119 (2008). https://doi.org/10.1007/s00778-007-0053-2
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DOI: https://doi.org/10.1007/s00778-007-0053-2