I/O Complexity for Range Queries on Region Data Stored Using an R-tree

In this paper we study the node distribution of an Rtree storing region data, like for instance islands, lakes or human-inhabited areas. We will show that real region datasets are packed in minimum bounding rectangles (MBRs) whose area distribution follows the same power law, named REGAL (REGion Area Law) [12], as that for the regions themselves. Moreover, these MBRs are packed in their turn into MBRs following the same law, and so on iteratively, up to the root of the R-tree. Based on this observation, we are able to accurately estimate the search effort for range queries, the most prominent spatial operation, using a small number of easy-to-retrieve parameters. Experiments on a variety of real datasets (islands, lakes, human-inhabited areas) show that our estimation is accurate, enjoying a maximum geometric average relative error within 30%.