| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 97 === Rearrangeability of a multistage interconnection network (MIN) is that if the MIN can connect its N inputs to its N outputs in all N! possible ways, by rearranging the existing connections if required. In [8], Das formulated an elegant sufficient condition for the rearrangeability of a combined (2n − 1)-stage MIN, where n = logN, and presented an O(NlogN)-time routing algorithm for MINs that satisfy the sufficient condition. However, the above definition of rearrangeability and the results of Das are for electronic MINs. Recently, optical MINs have become a promising network choice for their high performance. As was mentioned in [28], the fundamental difference between an electronic MIN and an optical MIN is that: two routing requests in an electronic MIN can be sent simultaneously if they are link-disjoint, while two routing requests in an optical MIN can be sent simultaneously only when their routing paths are node-disjoint, meaning that these two paths do not pass through the same switching element and therefore there is no crosstalk problem. The purpose of this thesis is to redo the works of Das for optical MINs. In particular, we formulate a sufficient condition for the crosstalk-free rearrangeability of a combined (2n−2)-stage and a combined (2n−1)-stage optical MIN, we propose an O(N logN)-time routing algorithm for optical MINs that satisfy the sufficient condition. In this thesis we also propose an algorithm to realize any permutation in a baseline network with node-disjoint paths in four passes.
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