Vertex-Disjoint Paths in the Generalized Hypercube under 1-Restricted Connectivity

The generalized hypercube is an excellent interconnection network since it includes many interconnection topologies and it can be used to construct many data center networks. Considering the probability that, in general, all neighbors of one vertex becoming faulty at the same time is extremely low, we assume that each vertex has at least one fault-free neighbor. An r-dimensional generalized hypercube is denoted by G(m_r, m_r-1,⋅, m_1). In this paper, we proposed an efficient algorithm which can construct at least κ^1(G) disjoint paths based on any two adjacent vertices in G(m_r, m_r-1,˙, m_1) in O(rm) time where κ^1(G) is the 1-restricted connectivity of G(m_r, m_r-1,˙, m_1). The maximum length of these disjoint paths is bounded by 7.

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