• myGriffith
    • Staff portal
    • Contact Us⌄
      • Future student enquiries 1800 677 728
      • Current student enquiries 1800 154 055
      • International enquiries +61 7 3735 6425
      • General enquiries 07 3735 7111
      • Online enquiries
      • Staff phonebook
    View Item 
    •   Home
    • Griffith Research Online
    • Journal articles
    • View Item
    • Home
    • Griffith Research Online
    • Journal articles
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

  • All of Griffith Research Online
    • Communities & Collections
    • Authors
    • By Issue Date
    • Titles
  • This Collection
    • Authors
    • By Issue Date
    • Titles
  • Statistics

  • Most Popular Items
  • Statistics by Country
  • Most Popular Authors
  • Support

  • Contact us
  • FAQs
  • Admin login

  • Login
  • Fast Sequential and Parallel Algorithms for Finding Extremal Sets

    Author(s)
    Shen, Hong
    Evans, D.
    Griffith University Author(s)
    Shen, Hong
    Year published
    1996
    Metadata
    Show full item record
    Abstract
    We consider the problem of finding the minimal (maximal) sets of a family of sets that have no subset (superset) in the family. Given a family F of k sets with N elements and a domain of size n, first we show that using word-to-bit mapping, a technique of compressing ^ords into bits and processing bits instead of words, we can obtain a simple algorithm tlfiat solves this problem in [ILM0001] time using [ILM0002] space in the worst case. When [ILM0003], our algorithm runs in O(N 2/log2 N) time and O(N 2/log3 N) space, thus improving known results. We then present two fasif parallel algorithms for solving this problem - an ...
    View more >
    We consider the problem of finding the minimal (maximal) sets of a family of sets that have no subset (superset) in the family. Given a family F of k sets with N elements and a domain of size n, first we show that using word-to-bit mapping, a technique of compressing ^ords into bits and processing bits instead of words, we can obtain a simple algorithm tlfiat solves this problem in [ILM0001] time using [ILM0002] space in the worst case. When [ILM0003], our algorithm runs in O(N 2/log2 N) time and O(N 2/log3 N) space, thus improving known results. We then present two fasif parallel algorithms for solving this problem - an O(log N) time algorithm using [ILM0004] processors on a CREW PRAM and a constant-time algorithm using [ILM0005] processors on a combining CRCW PRAM in which concurrent writing is resolved by writing the sum of the individual values to be written. These <kre respectively the first NC algorithm on the CREW and constant-time algorithm on the CRCW for the extremal set problem. Finally we extend the extremal set problem to the case when F contains multisets, and show that in this case the problem can b<b solved in [ILM0006] time and O (N + (k 2/log N)) space when the maximal number ofduplicates of any element within a multiset is m and all duplicates are uniformly distributed.
    View less >
    Journal Title
    International Journal of Computer Mathematics
    Volume
    61
    Issue
    3-4
    DOI
    https://doi.org/10.1080/00207169608804512
    Subject
    Applied mathematics
    Landscape ecology
    Theory of computation
    Publication URI
    http://hdl.handle.net/10072/120756
    Collection
    • Journal articles

    Footer

    Disclaimer

    • Privacy policy
    • Copyright matters
    • CRICOS Provider - 00233E
    • TEQSA: PRV12076

    Tagline

    • Gold Coast
    • Logan
    • Brisbane - Queensland, Australia
    First Peoples of Australia
    • Aboriginal
    • Torres Strait Islander