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The Cost of Cache-Oblivious Searching

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Stony Brook University, Stony Brook, NY, 11794-4400, USA

    Michael A. Bender

  2. Tokutek Inc., Lexington, MA, USA

    Michael A. Bender

  3. MADALGO—Center for Massive Data Algorithmics, a Center of the Danish National Research Foundation, Department of Computer Science, Aarhus University, Ny Munkegade, 8000, Århus C, Denmark

    Gerth Stølting Brodal

  4. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Rolf Fagerberg

  5. Department of Management Science and Engineering, Antai School of Economics and Management, Shanghai JiaoTong University, Shanghai, 200052, China

    Dongdong Ge

  6. Department of System Engineering and Engineering Management, Chinese University of Hongkong, Hongkong, China

    Simai He

  7. Networking and Device Connectivity at Windows Division, Microsoft, Redmond, WA, 98052, USA

    Haodong Hu

  8. Department of Computer and Information Science, Polytechnic University, Brooklyn, NY, 11201, USA

    John Iacono

  9. School of Computer Science, University of Waterloo, Waterloo, Ontarion, N2L 3G1, Canada

    Alejandro López-Ortiz

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  1. Michael A. Bender
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Correspondence to Alejandro López-Ortiz.

Additional information

An earlier version of this paper in extended abstract form appears in the Proceedings of the 44th Annual Symposium on the Foundations of Computer Science (FOCS), pages 271–280, 2003 [13].

M.A. Bender was supported in part by NSF Grants CCF 0621439/0621425, CCF 0540897/05414009, CCF 0634793/0632838, CNS 0627645, and CCF 0937822 and by DOE Grant DE-FG02-08ER25853.

G.S. Brodal was partially supported by the Future and Emerging Technologies programme of the EU under contract number IST-1999-14186 (ALCOM-FT) and the Carlsberg Foundation (contract number ANS-0257/20).

J. Iacono was supported in part by NSF grants CCF-0430849 and OISE-0334653 and by an Alfred P. Sloan Fellowship.

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Bender, M.A., Brodal, G.S., Fagerberg, R. et al. The Cost of Cache-Oblivious Searching. Algorithmica 61, 463–505 (2011). https://doi.org/10.1007/s00453-010-9394-0

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