這篇論文中,我們探討Banyan型網路在干擾限制下的可重排性. 令n,x,p和c是非負整數且滿足x和c介於0到n之間, 然後n和p大於等於1. Banyan型網路是一個有2的n+1次方個輸入端和2的n+1次方個輸出端和額外加x層的Banyan型網路且滿足每一個連通包含至多c個連接器受到干擾.(註:兩個訊息進入相同的連接器,我們稱為干擾)我們給予Banyan型網路在干擾限制下的可重排性的充分必要條件.

In the thesis, we study the rearrangeability of the Banyan-type
network with crosstalk constraint. Let $x$, $p$ and $c$ be
nonnegative integers with $0leq x,cleq n$ and $n,pgeq 1$.
$B_{n}(x,p,c)$ 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 switch elements. We give the
necessary and sufficient conditions for rearrangeable
Banyan-type networks $B_{n}(x,p,c)$.

Contents
1 Introduction ............................1
2 Some preliminaries ......................6
3 The main results ........................8

[1] V.E. Benes, Mathematical theory of connecting networks and telephone traffic, New York: Academic, 1965.
[2] J.C. Bermond, J.M. Fourneau, A. Jean-Marie, Equivalence of multistage interconnection networks, Inform. Process Lett. 26(1), 45-50, 1987.
[3] G.J. Chang, F.K. Huang, L.D. Tong, Characterizing bit permutation networks, Networks 33, 261-267, 1999.
[4] G.R. Goke, G.J. Lipovski, Banyan networks for partitioning multiprocessors systems, Proc. 1st Annu. Symp. Comp. Arch., 21-28, 1973.
[5] F.K. Hwang, Superior channel graphs, Proc. 9th Internat. Teletraffic Congr., Torremolinos, Spain, 1979.
[6] F.K. Hwang, The mathematical theory of nonblocking switching networks, 2nd Edition, World Scienti‾c, 2004.
[7] A. Jajszczyk, A simple algorithm for the control of rearrangeable switching networks, IEEE Transactions on communications, vol. 33, 168-171, 1985.
[8] C.T. Lea, Multi-$Log_{2}N$ networks and their applications in high speed electronic and photonic switching systems, IEEE Transactions on communica-
tions, vol. 38, 1740-1749, 1990.
[9] J. Patel, Performance of processor-memory interconnections for multiprocessors, IEEE Transactions on computers, vol. C-30, 771-780, 1981.
[10] D.J. Shyy, C.T. Lea, Rearrangeable $Log_{2^{d}}(N,m,p)$ networks, IEEE Transactions on communications, vol. 42, no. 5, 2084-2086, 1994.
[11] L.D. Tong, F.K. Hwang, G.J. Chang, Channel graphs of bit permutation networks, Theoretical computer science 263, 139-143, 2001.
[12] M.M. Vaez, C.T. Lea, Strictly nonblocking directional-coupler-based switching networks under crosstalk Constraint, IEEE Transactions on communications, vol. 48, 316-323, 2000.
[13] M.M. Vaez, C.T. Lea, Wide-sense nonblocking Banyan-type switching systems based on directional couplers, IEEE J. Select. Areas communications, vol. 16, 1327-1332, 1998.
[14] D.B. West, Introduction to graph theory, 2nd Edition, Prentice-Hall, 2001.
[15] C.L. Wu, T.Y. Feng, On a class of multistage interconnection networks,IEEE Transactions on communications, vol. C-29, 694-702, 1980.