Computing the largest empty rectangle
SIAM Journal on Computing
Fast algorithms for computing the largest empty rectangle
SCG '87 Proceedings of the third annual symposium on Computational geometry
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Incremental distance join algorithms for spatial databases
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Multidimensional access methods
ACM Computing Surveys (CSUR)
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Determining the Convex Hull in Large Multidimensional Databases
DaWaK '01 Proceedings of the Third International Conference on Data Warehousing and Knowledge Discovery
Mining for empty spaces in large data sets
Theoretical Computer Science - Database theory
Query optimization by semantic reasoning
Query optimization by semantic reasoning
Algorithms for processing K-closest-pair queries in spatial databases
Data & Knowledge Engineering
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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.