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 6= ∅. 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.