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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

The Multicast Rearrangeability of Banyan-type Networks

Li, Yun-Ruei 28 July 2006 (has links)
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.

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