| Summary: | 博士 === 國立交通大學 === 資訊科學與工程研究所 === 97 === In many parallel computer systems, processors are connected on the basis of interconnection networks, referred to as networks henceforth. Among various kinds of networks, linear arrays and rings are widely applied in parallel and distributed computation. In particular, paths and cycles are two topological structures commonly used to model linear arrays and rings, respectively. Therefore we investigate how to embed paths and cycles into some interconnection networks in this thesis. Because the components of a network may fail not only accidentally but frequently, it is of great importance for a network to be capable of tolerating as many faults as possible. In this thesis the fault-tolerance related issues are also concerned. With the graph representation of an interconnection network, we can discuss these issues in a formal way.
Firstly, we study a family of super fault-tolerant hamiltonian networks, namely cycle composition networks. A k-regular hamiltonian and hamiltonian connected network is super fault-tolerant hamiltonian if it remains hamiltonian after removing up to k-2 vertices and/or edges and remains hamiltonian connected after removing up to k-3 vertices and/or edges. Super fault-tolerant hamiltonian networks have an optimal flavor with regard to fault-tolerant hamiltonicity and fault-tolerant hamiltonian connectivity. For this motivation, we observe that the cycle composition is an effective framework to construct a (k+2)-regular super fault-tolerant hamiltonian network on the basis of n k-regular super fault-tolerant hamiltonian networks, containing the same number of vertices, provided that n≥3 and k≥4.
Secondly, we investigate a variant of hamiltonian cycles, namely mutually independent hamiltonian cycles, on some interconnection networks. A set of hamiltonian cycles, having the same start vertex, is said to be mutually independent if any two of these hamiltonian cycles traverse different vertices at every time step except the start-up and termination. In this thesis, we show that the maximum number of mutually independent hamiltonian cycles can be embedded onto the binary wrapped butterfly network. Moreover, embedding mutually independent hamiltonian cycles onto faulty hypercubes and onto faulty star networks are also addressed.
Next, we investigate the conditional-fault tolerance of hypercubes. There is one thing worth noting. That is, if components of a network fail independently, then it is unlikely that all failures would be close to each other. When faulty vertices are concerned, it is reasonable to require that every vertex should have at least g fault-free neighbors. Analogously, when faulty edges are concerned, it can be assumed that every vertex is still incident to at least g fault-free edges. In this thesis we first study the fault diameter of the n-cube only for g=1, and then we explore the feasibility of fault-tolerant path embedding on hypercubes when g=2.
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