| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 98 === In [5, 7], Masuyama et al. proposed two all-to-all communication algorithms for chordal ring networks of degree 3. The ¯rst algorithm (call it Algorithm A) is
an all-to-all personalized exchange algorithm and it is used when there is no fault. The second algorithm (call it Algorithm B) is an all-to-all broadcast algorithm and
it can tolerate one or two faults. In [5, 7], it has been proven that Algorithm A takes sigma_i=1 to N/2 i time units to fulfill an all-to-all personalized exchange in a chordal ring network CR(N;w), where N is the number of nodes and w is the chord length of the chordal ring network. However, we observe that Algorithm A only utilizes ring-links to fulfill an all-to-all communication and Algorithm B tilizes chordal-links only when there are faults. Since all of the chordal-links are not used in any all-to-all communication when there is no fault, a huge amount of hardware is wasted. In this thesis, we will use chordal-links to facilitate an all-to-all personalized exchange.
In particular, we propose an all-to-all personalized exchange algorithm that works for all chordal ring networks. We will show that our algorithm uses less time units to fulfill an all-to-all personalized exchange and hence improves Algorithm A. We also provide an all-to-all personalized exchange algorithm that works only for chordal
ring networks with w = 3 and clarify some unclear parts and correct some incorrect parts in Algorithm B.
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