Cache-oblivious dynamic dictionaries with update/query tradeoffs

Gerth Stølting Brodal, Erik D. Demaine, Jeremy T. Fineman, John Iacono, Stefan Langerman, J. Ian Munro

    Research output: Chapter in Book/Report/Conference proceedingConference contribution


    Several existing cache-oblivious dynamic dictionaries achieve O(log B N) (or slightly better O(logB N/M)) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is the block size, which matches the classic B-tree data structure. One recent structure achieves the same query bound and a sometimes-better amortized update bound of O (1/Bθ(1/log log B)2) logB N + 1/B log2 N) memory transfers. This paper presents a new data structure, the xDict, implementing predecessor queries in O(1/ε logB N/M) worst-case memory transfers and insertions and deletions in O (1/εB 1-ε logB N/M) amortized memory transfers, for any constant ε with 0 < ε < 1. For example, the xDict achieves subconstant amortized update cost when N = M B°(B1-ε), whereas the B-tree's Θ(logB N/M) is subconstant only when N = o(MB), and the previously obtained Θ (1/BΘ(1/(log log B)2) logB N + 1/B log2 N) is subconstant only when N = o(2√B). The xDict attains the optimal tradeoff between insertions and queries, even in the broader external-memory model, for the range where inserts cost between Ω(1/B lg1+ε N) and O(1/lg3 N) memory transfers.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms
    PublisherAssociation for Computing Machinery (ACM)
    Number of pages9
    ISBN (Print)9780898717013
    StatePublished - 2010
    Event21st Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, TX, United States
    Duration: Jan 17 2010Jan 19 2010

    Publication series

    NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


    Other21st Annual ACM-SIAM Symposium on Discrete Algorithms
    Country/TerritoryUnited States
    CityAustin, TX

    ASJC Scopus subject areas

    • Software
    • General Mathematics


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