Cache-oblivious r-trees

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( N/B+T/B) memory transfers and a point query using O((N/B)ε) mem-ory transfers for any ε> 0, where B is the block size of mem-ory 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 boun