Fault-tolerant Simulation of a Class of Regular Graphs in Hypercubes and Incrementally Extensible Hypercubes

• Main Authors: Shih-Jung Wu, 武士戎
• Other Authors: Huan-Chao Keh
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/68350016588012720764

博士 === 淡江大學 === 資訊工程學系博士班 === 94 === The hypercube is a widely-used interconnection architecture in the parallel machine. The Incrementally Extensible Hypercube (IEH), which is derived from the hypercube, is a generalization of interconnection network. Unlike the hypercube, the IEH can be constructed for any number of nodes. In other words, the IEH is incrementally expandable. In this thesis, the problem of embedding and reconfiguring some regular structures is considered in an IEH with faulty nodes. In recent years, the Fibonacci cube is a new interconnection architecture derived from hypercube. It also has some properties differ from hypercube. Thus we discuss the embedding of Fibonacci cube into the faulty hypercube. Some fault-tolerant embedding algorithms are proposed in this thesis. First, the algorithm in the present study enables us to obtain the good embedding of a ring into a faulty IEH with 2-expansion. Such result can be tolerated up to (n+1) faults with congestion 1, load 1, and dilation 3. When we allow unbounded expansion, the result of embedding of a ring into a faulty IEH can be tolerated up to O(n*log2m) faults with congestion 1, load 1, and dilation 4. The embedding methods in the study are mainly optimized for balancing the processor loads, under the situation of minimizing dilation and congestion as far as possible. Next we consider embedding of mesh into faulty IEH. In 2-expansion, it can be tolerated (n+1) faults with dilation 3, congestion 1, and load 1. Moreover, it can be tolerated up to O(n2-(r+s)2) in unbounded expansion. We discuss embedding of a complete binary tree into faulty IEH in the third. The cost is dilation 4, congestion 1, and load 1. In 2-expansion and unbounded expansion, embedding of a complete binary tree into faulty IEH can be tolerated (n+1) and O(n2-h2) faults. Finally, embedding of Fibonacci cube into faulty hypercube with dilation 3, congestion 2, load 1, unbounded expansion and O(m2-n2) faults can be tolerated, induced by our algorithm.