Cache-oblivious R-trees

Lars Arge, Mark de Berg, Herman Haverkort

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

13 Citations (Scopus)


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 5 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) e) 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.

Original languageEnglish
Title of host publicationSCG '05: Proceedings of the twenty-first annual symposium on Computational geometry, June 2005
PublisherAssociation for Computing Machinery, Inc
Number of pages10
Publication statusPublished - 2005
Event21st Annual Symposium on Computational Geometry, SCG'05 - Pisa, Italy
Duration: 6 Jun 20058 Jun 2005


Conference21st Annual Symposium on Computational Geometry, SCG'05


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


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