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URN etd-0901103-160053
Author Jyh-Wen Mao
Author's Email Address No Public.
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Department Applied Mathematics
Year 2002
Semester 2
Degree Ph.D.
Type of Document
Language English
Title The Coloring and Routing Problems on de Bruijn
Interconnection Networks
Date of Defense 2003-07-18
Page Count 105
Keyword
  • routing
  • coloring
  • fault-tolerant
  • de Bruijn graph
  • Abstract de Bruijn graphs are attractive due to its simplicity of routing messages between two nodes and the capability of fault tolerance. The shortest path from a node V to a node W in the directed binary de Bruijn graph can be obtained by firstly determining the longest substring, common to the right/left of V and to the left/right of W. Then L-operations/R-operations are performed to finish this routing process. However, this method does not always find the shortest path in the undirected binary de Bruijn graph. In this dissertation, we propose a shortest path routing algorithm which requires O(m2) time. We also design a fault-tolerant routing algorithm which provides the shortest path and another node-disjoint path of length at most m + log2m + 4. Our algorithm can tolerate one node failure in the m-dimensional binary de Bruijn network.
    In concurrent systems, a 1-fair alternator design is optimal if each processor can execute the critical step once in the fewest steps. This problem corresponds to use the minimum number of colors to color the processors in the system. Thus, the optimal
    design of a 1-fair alternator problem can be transformed into the coloring problem. We propose a simple and fast algorithm to solve the node coloring problem on the undirected binary de Bruijn graph. In our algorithm, the number of colors used is 3, and it is an optimal design. We also extend our method to solve the coloring problem on k-ary de Bruijn graphs. We first present a simple algorithm which needs 2k colors. By slight improvement, the number of required colors is reduced to k+1.
    Advisory Committee
  • Lih-Hsing Hsu - chair
  • Chuan-Yi Tang - co-chair
  • Xuding Zhu - co-chair
  • SingLing Lee - co-chair
  • Yaw-Ling Lin - co-chair
  • Ce-Kuen Shieh - co-chair
  • Gen-Huey Chen - co-chair
  • Chang-Biau Yang - advisor
  • Files
  • etd-0901103-160053.pdf
  • indicate access worldwide
    Date of Submission 2003-09-01

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