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

    Abstract

    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)
    Pages1448-1456
    Number of pages9
    ISBN (Print)9780898717013
    DOIs
    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

    Other

    Other21st Annual ACM-SIAM Symposium on Discrete Algorithms
    CountryUnited States
    CityAustin, TX
    Period1/17/101/19/10

    ASJC Scopus subject areas

    • Software
    • Mathematics(all)

    Fingerprint Dive into the research topics of 'Cache-oblivious dynamic dictionaries with update/query tradeoffs'. Together they form a unique fingerprint.

  • Cite this

    Brodal, G. S., Demaine, E. D., Fineman, J. T., Iacono, J., Langerman, S., & Munro, J. I. (2010). Cache-oblivious dynamic dictionaries with update/query tradeoffs. In Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 1448-1456). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery (ACM). https://doi.org/10.1137/1.9781611973075.117