| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 96 === Previous all-to-all personalized exchange algorithms are mainly for hypercube, mesh, and torus. In [17], Yang andWang first proposed an all-to-all personalized ex-
change algorithm for multistage interconnection networks (MINs). Their algorithm is optimal and works for a class of unique-path, self-routable MINs (for example, baseline, omega, banyan networks). Do notice that all the MINs considered in [17] must have the unique-path property and must satisfy N = 2n+1, in which N is the number of inputs (outputs), 2 means all the switches are of size 2 × 2, and n + 1 is the number of stages in the MINs. To our knowledge, no one has studied all-to-all personalized exchange in MINs which do not have the unique-path property and do not satisfy N = 2^(n+1). In [12], Padmanabhan proposed the generalized shuffle-exchange network (GSEN), which allows N != 2^(n+1) (thus N can be any even number). A GSEN becomes an omega network (i.e., the shuffle-exchange network) when N = 2^(n+1). Since a GSEN is not necessarily a unique-path MIN, Yang and Wang’s optimal algorithm may not apply. The purpose of this thesis is to propose two optimal all-to-all personalized exchange algorithms for GSENs. Unlike Yang and Wang’s algorithm, we abandon the the requirement on the unique-path. The first algorithm uses the stage control technique and works for all even N. We will prove it is optimal when the stage control technique is assumed. On the contrary, the second algorithm does not use the stage control technique and works for all N such that N ≡ 2 (mod 4). We will prove that it is optimal.
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