Priority R-tree

The Priority R-tree is a worst-case asymptotically optimal alternative to the spatial tree R-tree. It was first proposed by Arge, De Berg, Haverkort and Yi, K. in an article from 2004.^[1] The prioritized R-tree is essentially a hybrid between a k-dimensional tree and a R-tree in that it defines a given object's N-dimensional bounding volume (called Minimum Bounding Rectangles – MBR) as a point in N-dimensions, represented by the ordered pair of the rectangles. The term prioritized arrives from the introduction of four priority-leaves that represents the most extreme values of each dimensions, included in every branch of the tree. Before answering a window-query by traversing the sub-branches, the prioritized R-tree first checks for overlap in its priority nodes. The sub-branches are traversed (and constructed) by checking whether the least value of the first dimension of the query is above the value of the sub-branches. This gives access to a quick indexation by the value of the first dimension of the bounding box.

Arge et al. writes that the priority tree always answers window-queries with ${\displaystyle O\left(\left({\frac {N}{B}}\right)^{1-{\frac {1}{d}}}+{\frac {T}{B}}\right)}${\displaystyle O\left(\left({\frac {N}{B}}\right)^{1-{\frac {1}{d}}}+{\frac {T}{B}}\right)} I/Os, where N is the number of d-dimensional (hyper-) rectangles stored in the R-tree, B is the disk block size, and T is the output size.

In the case of ${\displaystyle d=2}${\displaystyle d=2} the rectangle is represented by ${\displaystyle ,円((x_{min},y_{min}),(x_{max},y_{max}))}${\displaystyle ,円((x_{min},y_{min}),(x_{max},y_{max}))} and the MBR thus four corners ${\displaystyle ,円(x_{min},y_{min},x_{max},y_{max})}${\displaystyle ,円(x_{min},y_{min},x_{max},y_{max})}.

• Bounding volume hierarchy
• B-tree
• R-tree

• R-tree
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