An Algorithm to Find Optimal Independent Spanning Trees on Twisted-Cubes

Multiple independent spanning trees have applications to fault tolerance and data broadcasting in distributed networks. There is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex. The conjecture has been confirmed only for n-connected graphs with n=4, and it is still open for arbitrary n-connected graphs when n ≥ 5. In this paper, we provide a construction algorithm to find n independent spanning trees for the n-dimensional twisted-cube TNn, where N denotes the number of vertices in TNn. And for n ≥ 3, the height of each indepen- dent spanning tree on TNn is n+1.

[1]  S. N. Maheshwari,et al.  Finding Nonseparating Induced Cycles and Independent Spanning Trees in 3-Connected Graphs , 1988, J. Algorithms.

[2]  Jie Wu,et al.  Embedding of binomial trees in hypercubes with link faults , 1997, Proceedings of the 1997 International Conference on Parallel Processing (Cat. No.97TB100162).

[3]  Alon Itai,et al.  The Multi-Tree Approach to Reliability in Distributed Networks , 1988, Inf. Comput..

[4]  Parameswaran Ramanathan,et al.  Reliable Broadcast in Hypercube Multicomputers , 1988, IEEE Trans. Computers.

[5]  Jou-Ming Chang,et al.  Reducing the Height of Independent Spanning Trees in Chordal Rings , 2007, IEEE Transactions on Parallel and Distributed Systems.

[6]  Andreas Huck.  Independent Trees in Planar Graphs Independent trees , 1999, Graphs Comb..

[7]  Koji Obokata,et al.  Independent Spanning Trees of Product Graphs and Their Construction , 1996 .

[8]  Sun-Yuan Hsieh,et al.  Constructing edge-disjoint spanning trees in locally twisted cubes , 2009, Theor. Comput. Sci..

[9]  Alon Itai,et al.  Three tree-paths , 1989, J. Graph Theory.

[10]  Xiaola Lin,et al.  The t/k-diagnosability of the BC graphs , 2005, IEEE Transactions on Computers.

[11]  Yue-Li Wang,et al.  Optimal Independent Spanning Trees on Hypercubes , 2004, J. Inf. Sci. Eng..

[12]  Yoshihide Igarashi,et al.  Reliable broadcasting in product networks , 1998, Discret. Appl. Math..

[13]  Hiroshi Nagamochi,et al.  Independent spanning trees with small depths in iterated line digraphs , 2001, Discret. Appl. Math..

[14]  Deqiang Wang,et al.  The twisted-cube connected networks , 2008, Journal of Computer Science and Technology.

[15]  Chiuyuan Chen,et al.  Constructing Independent Spanning Trees for Hypercubes and Locally Twisted Cubes , 2009, 2009 10th International Symposium on Pervasive Systems, Algorithms, and Networks.

[16]  Yuh-Shyan Chen,et al.  Multi-node broadcasting in all-ported 3-D wormhole-routed torus using an aggregation-then-distribution strategy , 2004, J. Syst. Archit..

[17]  Yoshihide Igarashi,et al.  Broadcasting in Hypercubes with Randomly Distributed Byzantine Faults , 1994, WDAG.

[18]  S. Lennart Johnsson,et al.  Optimum Broadcasting and Personalized Communication in Hypercubes , 1989, IEEE Trans. Computers.

[19]  Selim G. Akl,et al.  Edge-Disjoint Spanning Trees on the Star Network with Applications to Fault Tolerance , 1996, IEEE Trans. Computers.