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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0728106-144313 |
| Date | 28 July 2006 |
| Creators | Li, Yun-Ruei |
| Contributors | none, Xuding Zhu, D. J. Guan, none, Li-Da Tong |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0728106-144313 |
| Rights | withheld, Copyright information available at source archive |
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