Abstract
The existence of parallel node-disjoint paths between any pair of nodes is a desirable property of interconnection networks, because such paths allow tolerance to node and/or link failures along some of the paths, without causing disconnection. Additionally, node-disjoint paths support high-throughput communication via the concurrent transmission of parts of a message. We characterize maximum-sized families of parallel paths between any two nodes of alternating group networks. More specifically, we establish that in a given alternating group network AN n , there exist n−1 parallel paths (the maximum possible, given the node degree of n−1) between any pair of nodes. Furthermore, we demonstrate that these parallel paths are optimal or near-optimal, in the sense of their lengths exceeding the internode distance by no more than four. We also show that the wide diameter of AN n is at most one unit greater than the known lower bound D+1, where D is the network diameter.
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Zhou, S., Xiao, W. & Parhami, B. Construction of vertex-disjoint paths in alternating group networks. J Supercomput 54, 206–228 (2010). https://doi.org/10.1007/s11227-009-0304-7
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DOI: https://doi.org/10.1007/s11227-009-0304-7