| Summary: | 博士 === 國立臺灣大學 === 資訊工程學研究所 === 88 === The arrangement graph, which represents a family of scalable graphs, is a generalization of the star graph. There are two parameters, denoted by n and k, for the arrangement graph, where 1kn-1. An (n, k)-arrangement graph, which is denoted by An,k, has vertices corresponding to the arrangements of k numbers out of the set {1, 2, ..., n}. In this thesis, a fault-free Hamiltonian path is embedded between arbitrary two distinct vertices of a faulty arrangement graph. The fault tolerance is summarized as follows.
(1) When n-k>6 and k5, at most k(n-k)-2 edge faults can be tolerated. There is an exception in which at most k(n-k)-3edge faults can be tolerated.
(2) When n-k>6 and k{2, 3, 4}or n-k=6 and k2, at most k(n-k-5) edge faults can be tolerated.
(3) When k{3, 4, 5} and k2, at most k edge faults can be tolerated.
(4) When n-k=2 and k2 , at most k-3 edge faults can be tolerated.
(5) When n-k2 and k=1, at most n-4 edge faults can be tolerated.
(6) When n-k5 and k2, at most k(n-k)-3k vertex faults can be tolerated.
(7) When n-k{3, 4} and k2, at most n-3 vertex faults can be tolerated.
(8) When n-k=2 and k2, at most k-3 vertex faults can be tolerated.
(9) When n-k3, at most k (vertex or edge) faults can be tolerated.
(10) When n-k=2, at most k-3 (vertex or edge) faults can be tolerated.
A new embedding method, based on a backtracking technique, is proposed in this thesis. This thesis makes a significant improvement over a previous work by Hsieh et al.
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