Optimal routing algorithm and diameter in hexagonal torus networks

Authors:
Zhen Zhang;Wenjun Xiao;Mingxin He
Affiliations:
Dept. of Computer Science, South China University of Technology, Guangzhou, China and Dept. of Computer Science, Jinan University, Guangzhou, China;Dept. of Computer Science, South China University of Technology, Guangzhou, China;Dept. of Computer Science, South China University of Technology, Guangzhou, China and Dept. of Computer Science, Jinan University, Guangzhou, China
Venue:
APPT'07 Proceedings of the 7th international conference on Advanced parallel processing technologies
Year:
2007

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Abstract

Nodes in the hexagonal mesh and torus network are placed at the vertices of a regular triangular tessellation, so that each node has up to six neighbors. The routing algorithm for the Hexagonal Torus is very complicated, and it is an open problem by now. Hexagonal mesh and torus are known to belong to the class of Cayley digraphs. In this paper, we use Cayley-formulations for the hexagonal torus, along with some result on subgraphs and Coset graphs, to develop the optimal routing algorithm for the Hexagonal Torus, and then we draw conclusions to the network diameter of the Hexagonal Torus.