Finding the Largest Empty Rectangle Containing Only a Query Point in Large Multidimensional Databases
Given a two-dimensional space, let S be a set of points stored in an R-tree, let R be the minimum rectangle containing the elements of S, and let q be a query point such that q ∉ S and R ∩ q ≠ ∅. In this paper, we present an algorithm for finding the empty rectangle with the largest area, sides parallel to the axes of the space, and containing only the query point q. The idea behind algorithm is to use the points that define the minimum bounding rectangles (MBRs) of some internal nodes of the R-tree to avoid reading as many nodes of the R-tree as possible, given that a naive algorithm must access all of them. We present several experiments considering synthetic and real data. The results show that our algorithm uses around 0.71–38% of the time and around 3–4% of the main storage needed by previous computational geometry algorithms. Furthermore, to the best of our knowledge, this is the first work that solves this problem considering that the points are stored in an R-tree.
KeywordsGeographical Information System Main Memory Query Point Real Point Naive Approach
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- [ADM+10a]Augustine, J., Das, S., Maheshwari, A., Nandy, S.C., Roy, S., Sarvattomananda, S.: Recognizing the largest empty circle and axis-parallel rectangle in a desired location. CoRR, abs/1004.0558 (2010)Google Scholar
- [ADM+10b]Augustine, J., Das, S., Maheshwari, A., Nandy, S.C., Roy, S., Sarvattomananda, S.: Querying for the largest empty geometric object in a desired location. CoRR, abs/1004.0558v2 (2010)Google Scholar
- [Cor02]Corral, A.: Algoritmos para el Procesamiento de Consultas Espaciales utilizando R-trees. La Consulta de los Pares Más Cercanos y su Aplicación en Bases de Datos Espaciales. PhD thesis, Universidad de Almería, Escuela Politécnica Superior, España, Enero (2002)Google Scholar
- [DN11]De, M., Nandy, S.C.: Inplace algorithm for priority search tree and its use in computing largest empty axis-parallel rectangle. CoRR, abs/1104.3076 (2011)Google Scholar
- [Gut84]Guttman, A.: R-trees: A dynamic index structure for spatial searching. In: ACM SIGMOD Conference on Management of Data, pp. 47–57. ACM (1984)Google Scholar
- [HS98]Hjaltason, G.R., Samet, H.: Incremental distance join algorithms for spatial databases. In: ACM SIGMOD Conference on Management of Data, Seattle, WA, pp. 237–248 (1998)Google Scholar
- [Kin81]King, J.J.: Query optimization by semantic reasoning. PhD thesis, Stanford University, CA, USA (1981)Google Scholar
- [KS11]Kaplan, H., Sharir, M.: Finding the maximal empty rectangle containing a query point. CoRR, abs/1106.3628 (2011)Google Scholar
- [SC03]Shekhar, S., Chawla, S.: Spatial databases - a tour. Prentice Hall (2003)Google Scholar