# The Coloring and Routing Problems on de Bruijn Interconnection Networks

Abstract (Summary)

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.
Bibliographical Information:

Advisor:Yaw-Ling Lin; Chuan-Yi Tang; Chang-Biau Yang; Ce-Kuen Shieh; Lih-Hsing Hsu; SingLing Lee; Gen-Huey Chen; Xuding Zhu

School:National Sun Yat-Sen University

School Location:China - Taiwan

Source Type:Master's Thesis

Keywords:routing coloring fault tolerant de bruijn graph

ISBN:

Date of Publication:09/01/2003