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Algorithmica

, Volume 53, Issue 1, pp 50–68 | Cite as

Cache-Oblivious R-Trees

  • Lars Arge
  • Mark de Berg
  • Herman Haverkort
Article

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 more than a constant number of rectangles in S, we can construct, for any constant ε, a structure that answers a rectangle query using \(O(\sqrt{N/B}+T/B)\) memory transfers and a point query using O((N/B) ε ) memory transfers, where T is the number of reported rectangles and 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.

Keywords

I/O-efficiency Cache-oblivious data structures Geometric data structures R-trees 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.MADALGO, Department of Computer ScienceUniversity of Aarhus, IT-ParkenAarhus NDenmark
  2. 2.Department of Computer ScienceTU EindhovenMB EindhovenThe Netherlands

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