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 boundingbox hierarchy and as such it is the first cache-oblivious Rtree 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 ) 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 cacheaware structure. Categories and Subject Descriptors E.1 [Data]: Data structures; F.2 [Theory of computation]: Analys...

• Type: Conference
• Year: 2005
• Where: COMPGEOM
• Authors: Lars Arge, Mark de Berg, Herman J. Haverkort
• Keywords: COMPGEOM 2005, Discrete Geometry, Memory Transfers, Rectangle, Rectangle Query