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Computer Science > Data Structures and Algorithms

arXiv:1904.12370 (cs)
[Submitted on 28 Apr 2019 (v1), last revised 14 Oct 2019 (this
version, v2)]

Title:Compact Fenwick trees for dynamic ranking and selection

Authors:Stefano Marchini, Sebastiano Vigna
View a PDF of the paper titled Compact Fenwick trees for dynamic
ranking and selection, by Stefano Marchini and 1 other authors
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    Abstract:The Fenwick tree is a classical implicit data structure
    that stores an array in such a way that modifying an element,
    accessing an element, computing a prefix sum and performing a
    predecessor search on prefix sums all take logarithmic time. We
    introduce a number of variants which improve the classical
    implementation of the tree: in particular, we can reduce its size
    when an upper bound on the array element is known, and we can
    perform much faster predecessor searches. Our aim is to use our
    variants to implement an efficient dynamic bit vector: our
    structure is able to perform updates, ranking and selection in
    logarithmic time, with a space overhead in the order of a few
    percents, outperforming existing data structures with the same
    purpose. Along the way, we highlight the pernicious interplay
    between the arithmetic behind the Fenwick tree and the structure
    of current CPU caches, suggesting simple solutions that improve
    performance significantly.

Subjects: Data Structures and Algorithms (cs.DS)
Cite as:  arXiv:1904.12370 [cs.DS]
          (or arXiv:1904.12370v2 [cs.DS] for this version)
          https://doi.org/10.48550/arXiv.1904.12370
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Sebastiano Vigna [view email]
[v1] Sun, 28 Apr 2019 19:04:24 UTC (790 KB)
[v2] Mon, 14 Oct 2019 14:04:03 UTC (1,660 KB)
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