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Optimal Construction of All Shortest Node-Disjoint Paths in Hypercubes with Applications

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1 Author(s)
Cheng-Nan Lai ; Dept. of Inf. Manage., Nat. Kaohsiung Marine Univ., Kaohsiung, Taiwan

Routing functions had been shown effective in constructing node-disjoint paths in hypercube-like networks. In this paper, by the aid of routing functions, m node-disjoint shortest paths from one source node to other m (not necessarily distinct) destination nodes are constructed in an n-dimensional hypercube, provided the existence of such node-disjoint shortest paths which can be verified in O(mn1.5) time, where m ≤ n. The construction procedure has worst case time complexity O(mn), which is optimal and hence improves previous results. By taking advantages of the construction procedure, m node-disjoint paths from one source node to other m (not necessarily distinct) destination nodes in an n-dimensional hypercube such that their total length is minimized can be constructed in O(mn1.5 + m3n) time, which is more efficient than the previous result of O(m2n2.5 + mn3) time. Besides, their maximal length is also minimized in the worst case.

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Parallel and Distributed Systems, IEEE Transactions on  (Volume:23 ,  Issue: 6 )