none

When the number of nodes increases,
the chance that nodes or links fail increases. Then a fault-tolerant routing
method is important to maintian the performance of the system. In the
hypercube, safety levels and safety vectors provide the fault distribution
information used to guide routing fault-tolerantly. The safety vectors for the
hypercube describes the fault distribution more percisely than the safety
level. The concept of safety levels has been applied to the star graph by
other researchers. In this thesis, we apply the concept of the safety vectors
in the hypercube to the star graph, and define three different safety vectors,
including undirected safety vector, directed safety vector, and statistical
safety vector. We first show the ability of the undirected safety vector. Then
we extend the ideal to the directed safety vector and show it is better in
deciding routing paths than the safety level for the star graph. We also show
the reason that makes the directed safety vector not able to be used for
derouting. In the previous result, a little change can make the directed
safety vector usable for derouting in the hypercube. However, for the star
graph, we can use only the information of neighbors to perform derouting with
a slight modification in the directed safety vector. Then we set levels to the
routing ability using the statistical safety vector. Try to make it contain
more information of the fault distribution.

Chapter 1 Introduction
Chatper 2 Review of Local Information Based Fault-tolerant Routing Methods
2.1 Safety Level for the Hypercube
2.2 Safety Vector for the Hypercube
2.3 Safety Level for the Star Graph
Chapter 3 Fault-Tolerant Routing
3.1 Undirected Safety Vector
3.2 Directed Safety Vector
3.3 Length and Ranking
3.4 Statistical Safety Vector
Chapter 4 Conclusion

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