The Historical R-tree is a spatio-temporal access method aimed at the retrieval of window queries in the past. The concept behind the method is to keep an R-tree for each timestamp in history, but allow consecutive trees to share branches when the underlying objects do not change. New branches are only created to accommodate updates from the previous timestamp. Although existing implementations...

R-trees and related structures, like R-trees and R-trees, have been used to answer queries involving topological information about objects represented by their minimum bounding rectangles (MBRs). This paper describes how the R-tree method can be used for the storage and retrieval of direction relations. Direction relations deal with order in space, as for instance, left, above, north, southeast...

We begin with establishing properties of the unit revenue function, g(·). Lemma 6. 1. g(·) is a non-negative, continuous, non-decreasing, and concave function on R+, with g(0) = 0. 2. yg(1/y) is non-decreasing and concave on R++. 3. g(y)/y is non-increasing on R+. 4. If u, v > 0, then g(u) g(v) ≥ min( u v , 1), 1 u ∫ u 0 g(v)dv ≤ g(u/2). Proof. 1. That g(·) is non-negative, continuous and non-d...

The R-Tree and variant indexes have been used for multidimensional indexing since 1984 and applied to temporal data since 1994. Despite this, there are few functional implementations of the index that can be applied directly to the temporal data. This paper explores the use of the index for temporal subsequence searches and identifies two implications that must be considered so the index can be...