Issue No. 01 - Jan. (2016 vol. 27)
ISSN: 1045-9219
pp: 250-262
Tsung-Han Tsai , Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, R.O.C
Y-Chuang Chen , Department of Information Management, Minghsin University of Science and Technology, Xinfeng Hsinchu, Taiwan, R.O.C
Jimmy J. M. Tan , Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, R.O.C
ABSTRACT
Topological properties have become a popular and important area of focus for studies that analyze interconnections between networks. The hypercube is one of the most widely discussed topological structures for interconnections between networks and is usually covered in introductions to the basic principles and methods for network design. The exchanged hypercube $\textrm {EH}(s,t)$ is a new variant of the hypercube that has slightly more than half as many edges and retains several valuable and desirable properties of the hypercube. In this paper, we propose an approach for shortest path routing algorithms from the source vertex to the destination vertex in $\textrm {EH}(s,t)$ with time complexity $O(n)$ , where $n=s+t+1$ and $1\le s\le t$ . We focus on edge congestion, which is an important indicator for cost analyses and performance measurements in interconnection networks. Based on our shortest path routing algorithm, we show that the edge congestion of $\textrm {EH}(s,t)$ is $3\cdot 2^{s+t+1}-2^{s+1}-2^{t+1}$ . In addition, we prove that our shortest path routing algorithm is an optimal routing strategy with respect to the edge congestion of $\textrm {EH}(s,t)$ .
INDEX TERMS
Routing, Hypercubes, Algorithm design and analysis, Time complexity, Bipartite graph, Hamming distance
CITATION

T. Tsai, Y. Chen and J. J. Tan, "Optimal Edge Congestion of Exchanged Hypercubes," in IEEE Transactions on Parallel & Distributed Systems, vol. 27, no. 1, pp. 250-262, 2016.
doi:10.1109/TPDS.2014.2387284