, Volume 61, Issue 2, pp 463–505 | Cite as

The Cost of Cache-Oblivious Searching

  • Michael A. Bender
  • Gerth Stølting Brodal
  • Rolf Fagerberg
  • Dongdong Ge
  • Simai He
  • Haodong Hu
  • John Iacono
  • Alejandro López-OrtizEmail author


This paper gives tight bounds on the cost of cache-oblivious searching. The paper shows that no cache-oblivious search structure can guarantee a search performance of fewer than lg elog  B N memory transfers between any two levels of the memory hierarchy. This lower bound holds even if all of the block sizes are limited to be powers of 2. The paper gives modified versions of the van Emde Boas layout, where the expected number of memory transfers between any two levels of the memory hierarchy is arbitrarily close to [lg e+O(lg lg B/lg B)]log  B N+O(1). This factor approaches lg e≈1.443 as B increases. The expectation is taken over the random placement in memory of the first element of the structure.

Because searching in the disk-access machine (DAM) model can be performed in log  B N+O(1) block transfers, this result establishes a separation between the (2-level) DAM model and cache-oblivious model. The DAM model naturally extends to k levels. The paper also shows that as k grows, the search costs of the optimal k-level DAM search structure and the optimal cache-oblivious search structure rapidly converge. This result demonstrates that for a multilevel memory hierarchy, a simple cache-oblivious structure almost replicates the performance of an optimal parameterized k-level DAM structure.


Cache-oblivious B-tree Cache-oblivious searching van Emde Boas layout 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Michael A. Bender
    • 1
    • 2
  • Gerth Stølting Brodal
    • 3
  • Rolf Fagerberg
    • 4
  • Dongdong Ge
    • 5
  • Simai He
    • 6
  • Haodong Hu
    • 7
  • John Iacono
    • 8
  • Alejandro López-Ortiz
    • 9
    Email author
  1. 1.Department of Computer ScienceStony Brook UniversityStony BrookUSA
  2. 2.Tokutek Inc.LexingtonUSA
  3. 3.MADALGO—Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation, Department of Computer ScienceAarhus UniversityÅrhus CDenmark
  4. 4.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  5. 5.Department of Management Science and Engineering, Antai School of Economics and ManagementShanghai JiaoTong UniversityShanghaiChina
  6. 6.Department of System Engineering and Engineering ManagementChinese University of HongkongHongkongChina
  7. 7.Networking and Device Connectivity at Windows DivisionMicrosoftRedmondUSA
  8. 8.Department of Computer and Information SciencePolytechnic UniversityBrooklynUSA
  9. 9.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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