An efficient construction of one-to-many node-disjoint paths in folded hypercubes

A folded hypercube is basically a hypercube with additional links augmented, where the additional links connect all pairs of nodes with longest distance in the hypercube. In an n-dimensional folded hypercube, it has been shown that n+1 node-disjoint paths from one source node to other n+1 (mutually) distinct destination nodes, respectively, can be constructed in O(n^4) time so that their maximal length is not greater than @?n/2@?+1, where n+1 is the connectivity and @?n/2@? is the diameter. Besides, their maximal length is minimized in the worst case. In this paper, we further show that by minimizing the computations of minimal routing functions, these node-disjoint paths can be constructed in O(n^3) time, which is more efficient, and is hard to be reduced because it must take O(n^3) time to compute a minimal routing function by solving a corresponding maximum weighted bipartite matching problem with the best known algorithm.

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