Optimal Independent Spanning Trees on Odd Graphs

Authors:
Jong-Seok Kim;Hyeong-Ok Lee;Eddie Cheng;László Lipták
Affiliations:
School of Electrical Engineering and Computer Science, Yeungnam University, Gyeongsan, Korea 712-749;Department of Computer Education, Sunchon National University, Sunchon, Korea 540-742;Department of Mathematics and Statistics, Oakland University, Rochester, USA 48309;Department of Mathematics and Statistics, Oakland University, Rochester, USA 48309
Venue:
The Journal of Supercomputing
Year:
2011

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Abstract

The use of multiple independent spanning trees (ISTs) for data broadcasting in networks provides a number of advantages, including the increase of fault-tolerance and bandwidth. The designs of multiple ISTs on several classes of networks have been widely investigated. In this paper we show a construction algorithm of ISTs on odd graphs, and we analyze that all the lengths of the paths in the ISTs are less than or equal to the length of the shortest path+4, which is optimal. We also prove that the heights of the ISTs we constructed are d+1, which again is optimal, since the fault diameter of an odd graph is d+1.