Completely independent spanning trees in torus networks

Let T1, T2, …, Tk be spanning trees in a graph G. If for any two vertices u, v in G, the paths from u to v in T1, T2, …, Tk are pairwise internally disjoint, then T1, T2, …, Tk are completely independent spanning trees in G. Completely independent spanning trees can be applied to fault‐tolerant communication problems in interconnection networks. In this article, we show that there are two completely independent spanning trees in any torus network. Besides, we generalize the result for the Cartesian product. In particular, we show that there are two completely independent spanning trees in the Cartesian product of any 2‐connected graphs. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012

[1]  Robert E. Tarjan,et al.  A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees , 1985, Math. Oper. Res..

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

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

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

[5]  Richard Stong.  Hamilton decompositions of cartesian products of graphs , 1991, Discret. Math..

[6]  Andreas Huck.  Independent trees in graphs , 1994, Graphs Comb..

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

[8]  Hyeong-Ah Choi,et al.  Circuit-switched row-column broadcasting in torus and mesh networks , 1996, Networks.

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

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

[11]  S. Louis Hakimi,et al.  Disjoint Rooted Spanning Trees with Small Depths in deBruijn and Kautz Graphs , 1997, SIAM J. Comput..

[12]  D. W. Krumme,et al.  Diameter-preserving orientations of the torus , 1998 .

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

[14]  Yoshihide Igarashi,et al.  Independent Spanning Trees of Chordal Rings , 1999, Inf. Process. Lett..

[15]  Andreas Huck.  Independent Trees and Branchings in Planar Multigraphs , 1999, Graphs Comb..

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

[17]  Ran Libeskind-Hadas,et al.  On Edge-Disjoint Spanning Trees in Hypercubes , 1999, Inf. Process. Lett..

[18]  Toru Hasunuma,et al.  Completely independent spanning trees in the underlying graph of a line digraph , 2000, Discret. Math..

[19]  Douglas M. Blough,et al.  Multicast in Wormhole-Switched Torus Networks Using Edge-Disjoint Spanning Trees , 2001, J. Parallel Distributed Comput..

[20]  Toru Hasunuma,et al.  Completely Independent Spanning Trees in Maximal Planar Graphs , 2002, WG.

[21]  Biing-Feng Wang,et al.  Constructing Edge-Disjoint Spanning Trees in Product Networks , 2003, IEEE Trans. Parallel Distributed Syst..

[22]  Abderezak Touzene,et al.  Edge-disjoint spanning trees for the generalized butterfly networks and their applications , 2005, J. Parallel Distributed Comput..

[23]  Xingxing Yu,et al.  Finding Four Independent Trees , 2006, SIAM J. Comput..

[24]  Jou-Ming Chang,et al.  Parallel construction of optimal independent spanning trees on hypercubes , 2007, Parallel Comput..

[25]  Jean-Claude Bermond,et al.  Vertex disjoint routings of cycles over tori , 2007, Networks.

[26]  Jou-Ming Chang,et al.  On the independent spanning trees of recursive circulant graphs G(cdm, d) with d>2 , 2009, Theor. Comput. Sci..

[27]  Jou-Ming Chang,et al.  Independent Spanning Trees on Multidimensional Torus Networks , 2010, IEEE Transactions on Computers.

[28]  Matthias Kriesell,et al.  Balancing two spanning trees , 2011, Networks.