R-tree

Figure 1 highlights the problem of the lowx packed R-tree.

The R-tree obtained in the following way is nonsimplicial.

The Paris metric makes the plane into an R-tree.

R-tree: Typically the preferred method for indexing spatial data.

In the classic R-tree, objects are inserted into the subtree that needs the least enlargement.

Each geometry property is indexed using an R-tree.

Interval tree - A degenerate R-tree for one dimension (usually time).

Figure 3 illustrates some rectangles organized in a Hilbert R-tree.

A common real-world usage for an R-tree might be: "Find all museums within of my current location".

Each discrete tree can be regarded as an R-tree by a simple construction such that neighboring vertices have distance one.

The set of singular points is discrete, but fails to be closed since 1 is an ordinary point in this R-tree.

A plain R-tree splits a node on overflow, creating two nodes from the original one.

Each node of an R-tree has a variable number of entries (up to some pre-defined maximum).

Thus, the nodes of the resulting R-tree will be fully packed, with the possible exception of the last node at each level.

Ignorance of the y coordinate by the lowx packed R-tree tends to violate this empirical rule.

Thus, the space utilization is 100%; this structure is called a packed Hilbert R-tree.

The Hilbert R-tree has the following structure.

Minimal coverage reduces the amount of "dead space" (empty area) which is covered by the nodes of the R-tree.

In computer science, an X-tree is an index tree structure based on the R-tree used for storing data in many dimensions.

By adjusting the split policy, the Hilbert R-tree can achieve as high utilization as desired.

Roussopoulos and Leifker proposed a method for building a packed R-tree that achieves almost 100% space utilization.

The fact that the resulting father nodes cover little area explains why the lowx packed R-tree achieves excellent performance for point queries.

An R-tree is a uniquely arcwise-connected metric space in which every arc is isometric to some real interval.

This is a simple heuristic for constructing an R-tree with 100% space utilization which at the same time will have as good response time as possible.

Before answering a window-query by traversing the sub-branches, the prioritized R-tree first checks for overlap in its priority nodes.