There is a well-known conjecture on independent spanning trees (ISTs) on graphs: For any n-connected graph G with n≥1, there are n ISTs rooted at an arbitrary node on G. It still remains open for n≥5. We propose an integrated algorithm to construct n ISTs rooted at any node similar to 0 or 10n-1 on n-dimensional HCH cube for n≥1 and give the simulations of ISTs on several special BC networks, such as HCH cubes, crossed cubes, Möbius cubes, twisted cubes, etc.
-Independent spanning trees (ISTs for short) in networks have applications such as reliable communication protocols, the multi-node broadcasting, one-to-all broadcasting, reliable broadcasting, and secure message distribution. However, it is an open problem whether there are n ISTs rooted at any node in any n connected network with 5 n . In this paper, we consider the construction of ISTs in a family of hypercube variants, called conditional BC networks. A recursive algorithm based on two common rules is proposed to construct n ISTs rooted at any node in any n -dimensional conditional BC network n X . We also show that our constructive method is adaptive to not only the existing hypercube variants, but also some other ones.Index Terms -Conditional BC network, independent spanning trees, node-disjoint paths, recursive algorithm.
DCell has been proposed for enormous data centers as a server centric interconnection which can support millions of servers with high network capacity and provide good fault tolerance by only using commodity switches. In this paper, we study an attractive algorithm of finding Hamilton paths in dimensional. The time complexity of this algorithm is , where is the node number of DCellk .
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