Observations on MBC and MBR Approaches

Abstract

To expedite the processing of spatial queries, objects could be organized and indexed using the Sphere-tree index structure. Sphere-tree is a spatial access method used for storing and retrieving objects approximated by their MBCs; as opposed to the R-tree which is used for objects approximated by their MBRs. However, in order to utilize Sphere-tree to index MBCs we need to address the mismatch between approximation relations and actual relations for intermediate nodes of the tree. Intuitively, since MBC approximations of objects are different than their MBR approximations; we expected that this would change the rules of propagation in the intermediate nodes of Sphere-tree compared to those of R-tree. On the contrary, our investigations showed that the relations that may be satisfied between an intermediate node P and q’ (so that the node be selected for propagation in the Sphere-tree) are similar to those relations obtained for the case where R-tree was used in [64]. The same results were also obtained when investigating the empty results query optimization (i.e. where the result of the query is known to be empty without running the query [64]). These observations are described in detail in Sections 1 and 2.