Abstract
The problem of finding a nearest neighbor from a set of points in ℝd to a complex query object has attracted considerable attention due to various applications in computational geometry, bio-informatics, information retrieval, etc. We propose a generic method that solves the problem for various classes of query objects and distance functions in a unified way. Moreover, for linear space requirements the method simplifies the known approach based on ray-shooting in the lower envelope of an arrangement.
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References
Agarwal, P., Sharir, M.: Arrangements and their Applications. Handbook of Computational Geometry, pp. 49–119 (1998)
Agarwal, P.K., Matoušek, J.: On Range Searching with Semialgebraic Sets. Discrete and Computational Geometry 11(1), 393–418 (1994)
Chan, T.M.: Optimal Partition Trees. In: SCG 2010: Proceedings of the 2010 Annual Symposium on Computational Geometry, pp. 1–10. ACM (2010)
Chazelle, B.: The Discrepancy Method. Cambridge University Press (2000)
Chazelle, B., Welzl, E.: Quasi-optimal range searching in spaces of finite VC-dimension. Discrete and Computational Geometry 4(1), 467–489 (1989)
Cole, R., Yap, C.-K.: Geometric Retrieval Problems. In: FOCS 1983: Proceedings of the 24th Annual IEEE Symposium on Foundations of Computer Science, pp. 112–121 (1983)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry - Algorithms and Applications, 2nd edn. Springer (2000)
Haussler, D., Welzl, E.: Epsilon-nets and Simplex Range Queries. In: SCG 1986: Proceedings of the 2nd Annual Symposium on Computational Geometry, p. 71. ACM (1986)
Krauthgamer, R., Lee, J.: Navigating Nets: Simple Algorithms for Proximity Search. In: SODA 2004: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 798–807. ACM (2004)
Matoušek, J.: Construction of epsilon-Nets. Discrete & Computational Geometry 5, 427–448 (1990)
Matoušek, J.: Efficient Partition Trees. Discrete and Computational Geometry 8(1), 315–334 (1992)
Matoušek, J.: Geometric Discrepancy. Springer (1999)
Matoušek, J., Schwarzkopf, O.: On Ray shooting in Convex Polytopes. Discrete and Computational Geometry 10(1), 215–232 (1993)
Megiddo, N.: Applying Parallel Computation Algorithms in the Design of Serial Algorithms. Journal of the ACM 30(4), 852–865 (1983)
Mitra, P., Chaudhuri, B.B.: Efficiently computing the closest point to a query line. Pattern Recognition Letters 19(11), 1027–1035 (1998)
Mitra, P., Mukhopadhyay, A.: Computing a Closest Point to a Query Hyperplane in Three and Higher Dimensions. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds.) ICCSA 2003. LNCS, vol. 2669, pp. 787–796. Springer, Heidelberg (2003)
Mitra, P., Mukhopadhyay, A., Rao, S.V.: Computing the Closest Point to a Circle. In: CCCG 2003: Proceedings of the 15th Canadian Conference on Computational Geometry, pp. 132–135 (2003)
Mukhopadhyay, A.: Using simplicial partitions to determine a closest point to a query line. Pattern Recognition Letters 24(12), 1915–1920 (2003)
Schöngens, M., Hruz, T.: A Simple Framework for the Generalized Nearest Neighbor Problem. Technical Report 758, Theoretical Computer Science, ETH Zurich (2012)
Sharir, M., Shaul, H.: Ray Shooting Amid Balls, Farthest Point from a Line, and Range Emptiness Searching. In: SODA 2005: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 525–534 (2005)
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Hruz, T., Schöngens, M. (2012). A Simple Framework for the Generalized Nearest Neighbor Problem. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_8
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DOI: https://doi.org/10.1007/978-3-642-31155-0_8
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