• The KIPS Transactions:PartA
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• v.18A no.6
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• pp.225-232
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• 2011

Restricted Hypercube-Like (RHL) graphs are a graph class that widely includes useful interconnection networks such as crossed cube, Mobius cube, Mcube, twisted cube, locally twisted cube, multiply twisted cube, and generalized twisted cube. In this paper, we show that for an m-dimensional RHL graph G, $m{\geq}4$, with an arbitrary faulty edge set $F{\subset}E(G)$, ${\mid}F{\mid}{\leq}m-2$, graph $G{\setminus}F$ has a hamiltonian path between any distinct two nodes s and t if dist(s, V(F))${\neq}1$ or dist(t, V(F))${\neq}1$. Graph $G{\setminus}F$ is the graph G whose faulty edges are removed. Set V(F) is the end vertex set of the edges in F and dist(v, V(F)) is the minimum distance between vertex v and the vertices in V(F).

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.12
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• pp.4343-4355
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• 2014

Multicast group communication has many advantages in data centers and thus is widely used by many applications. It can efficiently reduce the network traffic and improve the application throughput. For the multicast application in data centers, an essential problem is how to find a minimal multicast tree, which has been proved to be NP-hard. In this paper, we propose an approximation tree-building method for the minimal multicast problem, named HD（Hamming Distance）-based multicast tree. Consider that many new network structures have been proposed for data centers. We choose three representative ones, including BCube, FBFLY, and HyperX, whose topological structures can be regarded as the generalized hypercube. Given a multicast group in BCube, the HD-based method can jointly schedule the path from each of receiver to the only sender among multiple disjoint paths; hence, it can quickly construct an efficient multicast tree with the low cost. The experimental results demonstrate that our method consumes less time to construct an efficient multicast tree, while considerably reduces the cost of the multicast tree compared to the representative methods. Our approach for BCube can also be adapted to other generalized hypercube network structures for data centers after minimal modifications.