Cache-oblivious B-trees

Michael A. Bender, Erik D. Demaine, Martin Farach-Colton

Research output: Contribution to journalArticlepeer-review

74 Scopus citations

Abstract

This paper presents two dynamic search trees attaining near-optimal performance on any hierarchical memory. The data structures are independent of the parameters of the memory hierarchy, e.g., the number of memory levels, the block-transfer size at each level, and the relative speeds of memory levels. The performance is analyzed in terms of the number of memory transfers between two memory levels with an arbitrary block-transfer size of B; this analysis can then be applied to every adjacent pair of levels in a multilevel memory hierarchy. Both search trees match the optimal search bound of ⊖(1 + log B+1 N) memory transfers. This bound is also achieved by the classic B-tree data structure on a two-level memory hierarchy with a known block-transfer size B. The first search tree supports insertions and deletions in ⊖(1 + log B+1 N) amortized memory transfers, which matches the B-tree's worst-case bounds. The second search tree supports scanning S consecutive elements optimally in ⊖(1 + S/B) memory transfers and supports insertions and deletions in ⊖(1 + log B+1 N + log 2 N/B) amortized memory transfers, matching the performance of the B-tree for B = Ω(log N log log N).

Original languageEnglish (US)
Pages (from-to)341-358
Number of pages18
JournalSIAM Journal on Computing
Volume35
Issue number2
DOIs
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Mathematics(all)

Keywords

  • Cache efficiency
  • Data structures
  • Memory hierarchy
  • Search trees

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