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  • Optimal algorithms for generalized searching in sorted matrices

    Author(s)
    Shen, Hong
    Griffith University Author(s)
    Shen, Hong
    Year published
    1997
    Metadata
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    Abstract
    We present a set of optimal and asymptotically optimal sequential and parallel algorithms for the problem of searching on an m × n sorted matrix in the general case when m⩽n. Our two sequential algorithms have a time complexity of 0(mlog(2nm)) which is shown to be optimal. Our parallel algorithm runs in 0(log(logmlog log m) log (2nm1-z)) time using m/log(logmlog logm) processors on a COMMON CRCW PRAM, where 0 ⩽ z < 1 is a monotonically decreasing function on m, which is asymptotically work-optimal. The two sequential algorithms differ mainly in the ways of matrix partitioning: one uses row-searching and the other applies ...
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    We present a set of optimal and asymptotically optimal sequential and parallel algorithms for the problem of searching on an m × n sorted matrix in the general case when m⩽n. Our two sequential algorithms have a time complexity of 0(mlog(2nm)) which is shown to be optimal. Our parallel algorithm runs in 0(log(logmlog log m) log (2nm1-z)) time using m/log(logmlog logm) processors on a COMMON CRCW PRAM, where 0 ⩽ z < 1 is a monotonically decreasing function on m, which is asymptotically work-optimal. The two sequential algorithms differ mainly in the ways of matrix partitioning: one uses row-searching and the other applies diagonal-searching. The parallel algorithm is based on some non-trivial matrix partitioning and processor allocation schemes. All the proposed algorithms can be easily generalized for searching on a set of sorted matrices.
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    Journal Title
    Theoretical Computer Science
    Volume
    188
    Issue
    1-2
    DOI
    https://doi.org/10.1016/S0304-3975(97)00027-3
    Subject
    Mathematical Sciences
    Information and Computing Sciences
    Publication URI
    http://hdl.handle.net/10072/121202
    Collection
    • Journal articles

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