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URN etd-0728106-144313
Author Yun-Ruei Li
Author's Email Address m932040031@student.nsysu.edu.tw
Statistics This thesis had been viewed 5069 times. Download 1477 times.
Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title The Multicast Rearrangeability of Banyan-type Networks
Date of Defense 2006-07-21
Page Count 49
Keyword
  • rearrangeability
  • multicast
  • Abstract In the thesis, we study the f-cast rearrangeability of the Banyan-type network with crosstalk constraint. Let n, j, x and c be nonnegative integers with 0leq jleq n+1, 0leq xleq n and f=2^{j}. B_{n}(x,p,c) is the Banyan-type network with, 2^{n+1} inputs, 2^{n+1} outputs, x extra-stages, and each connection containing at most c crosstalk switches. We give the necessary and sufficient condictions for f-cast rearrangeable Banyan-type networks B_{n}(x,p,c). We show that
    (a) B_{n}(0,p,0) is f-cast rearrangeable nonblocking if and only if pgeq2^{lceil frac{n+j+1}{2} rceil}.
    (b) B_{n}(0,p,c) is f-cast rearrangeable nonblocking if and only if pgeq2^{lfloorfrac{n+j+1}{2} rfloor} for 1leq cleq n+1.
    (c) B_{n}(x,p,0) is f-cast rearrangeable nonblocking if and only if pgeqmax{2^{j+1}, 2^{lceil frac{n+j-x+1}{2} rceil}} for 0leq jleq n.
    (d) B_{n}(x,p,c) is 2^{n+1}-cast rearrangeable nonblocking if and only if pgeq2^{n+1} for 0leq cleq n+x+1.
    (e) B_{n}(x,p,n+x+1) is f-cast rearrangeable nonblocking if and only if pgeqmax{2^{j}, 2^{lfloor frac{n+j-x+1}{2}
    rfloor}}.
    (f) B_{n}(n,p,c) is f-cast rearrangeable nonblocking if and only if pgeqleft{
    2^{j} & if n+1geq jgeq n.
    2^{lceil frac{j+1}{2} rceil} & if lfloor frac{j+1}{2}
    rfloorgeq jgeq0.
    for 1leq cleq n+x.
    (g) B_{n}(x^{prime},p,c) is f-cast rearrangeable nonblocking if and only if pgeqleft{
    2^{j} & if n+1geq jgeq n.
    2^{lfloor frac{n+j-x+1}{2} rfloor} & if lfloor frac{n+j-x+1}{2} rfloorgeq jgeq0.
    for 1leq cleq n+x and 1leq x^{prime}leq n-1.
    Advisory Committee
  • D. J. Guan - chair
  • none - co-chair
  • Xuding Zhu - co-chair
  • none - co-chair
  • Li-Da Tong - advisor
  • Files
  • etd-0728106-144313.pdf
  • indicate accessible in a year
    Date of Submission 2006-07-28

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