Abstract
The vast number of applications featuring multimedia and geometric data has made the R-tree a ubiquitous data structure in databases. A popular and fundamental operation on R-trees is nearest neighbor search. While nearest neighbor on R-trees has received considerable experimental attention, it has received somewhat less theoretical consideration. We study pruning heuristics for nearest neighbor queries on R-trees. Our primary result is the construction of non-trivial families of R-trees where k-nearest neighbor queries based on pessimistic (i.e. min-max) distance estimates provide exponential speedup over queries based solely on optimistic (i.e. min) distance estimates. The exponential speedup holds even when k = 1. This result provides strong theoretical evidence that min-max distance heuristics are an essential component to depth-first nearest-neighbor queries. In light of this, we also consider the time-space tradeoffs of depth-first versus best-first nearest neighbor queries and construct a family of R-trees where best-first search performs exponentially better than depth-first search even when depth-first employs min-max distance heuristics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Manolopoulos, Y., Nanopoulos, A., Papadopoulos, A.N., Theodoridis, Y.: R-Trees: Theory and Applications. In: Advanced Information and Knowledge Processing, 1st edn., Springer, Heidelberg (2006)
Papadopoulos, A., Manolopoulos, Y.: Performance of nearest neighbor queries in r-trees. In: Proceedings of the 6th International Conference on Database Theory, pp. 394–408 (1997)
Berchtold, S., Böhm, C., Keim, D.A., Krebs, F., Kriegel, H.P.: On optimizing nearest neighbor queries in high-dimensional data spaces. In: Van den Bussche, J., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 435–449. Springer, Heidelberg (2000)
Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 47–57 (1984)
Sellis, T., Roussopoulos, N., Faloutsos, C.: R+-tree: A dynamic index for multidimensional objects. In: Proceedings of the 13th International Conference on Very Large Databases, pp. 507–518 (1988)
Beckmann, N., Kriegel, H., Schneider, R., Seeger, B.: R*-tree: An efficient and robust access method for points and rectangles. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 322–331 (1990)
Hjaltason, G.R., Samet, H.: Distance browsing in spatial databases. ACM Transactions on Database Systems 24, 265–318 (1999)
Berchtold, S., Böhm, C., Keim, D.A., Kriegel, H.P.: A cost model for nearest neighbor search in high-dimensional data space. In: Proceedings of the Sixteenth ACM Symposium on Principles of Database Systems, pp. 78–86. ACM Press, New York (1997)
Roussopoulos, N., Kelley, S., Vincent, F.: Nearest neighbor queries. In: Proceedings ACM SIGMOD Internaiontal Conference on the Management of Data, pp. 71–79 (1995)
Böhm, C., Berchtold, S., Keim, D.A.: Searching in high-dimensional spaces: Index structures for improving the performance of multimedia databases. ACM Computing Surveys (CSUR) 33, 322–373 (2001)
Cheung, K.L., Fu, A.W.C.: Enhanced nearest neighbour search on the r-tree. SIGMOD Record 27, 16–21 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adler, M., Heeringa, B. (2008). Search Space Reductions for Nearest-Neighbor Queries. In: Agrawal, M., Du, D., Duan, Z., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2008. Lecture Notes in Computer Science, vol 4978. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79228-4_48
Download citation
DOI: https://doi.org/10.1007/978-3-540-79228-4_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79227-7
Online ISBN: 978-3-540-79228-4
eBook Packages: Computer ScienceComputer Science (R0)