## Cache-Oblivious R-Trees (2005)

Citations: | 11 - 3 self |

### BibTeX

@MISC{Arge05cache-obliviousr-trees,

author = {Lars Arge and Mark de Berg and Herman Haverkort},

title = {Cache-Oblivious R-Trees},

year = {2005}

}

### OpenURL

### Abstract

We develop a cache-oblivious data structure for storing a set S of N axis-aligned rectangles in the plane, such that all rectangles in S intersecting a query rectangle or point can be found efficiently. Our structure is an axis-aligned bounding-box hierarchy and as such it is the first cache-oblivious R-tree with provable performance guarantees. If no point in the plane is contained in B or more rectangles in S, the structure answers a rectangle query using O(\sqrt{N/B} + T/B) memory transfers and a point query using O((N/B)^ε) memory transfers for any ε>0, where B is the block size of memory transfers between any two levels of a multilevel memory hierarchy. We also develop a variant of our structure that achieves the same performance on input sets with arbitrary overlap among the rectangles. The rectangle query bound matches the bound of the best known linear-space cache-aware structure.