Paired 2-disjoint path covers of k-ary n-cubes under the partitioned edge fault model

Abstract

The k-ary n-cube $Q_n^k$ serves as an indispensable interconnection network in the design of data center networks, network-on-chips, and parallel computing systems since it possesses numerous attractive properties. In these parallel architectures, the paired (or unpaired) many-to-many m-disjoint path cover (m-DPC) plays a significant role in message transmission. Nevertheless, the construction of m-DPC is severely obstructed by large-scale edge faults due to the rapid growth of the system scale. In this paper, we investigate the existence of paired 2-DPC in $Q_n^k$ under the partitioned edge fault (PEF) model, which is a novel fault model for enhancing the networks' fault-tolerance related to path embedding problem. We exploit this model to evaluate the edge fault-tolerance of $Q_n^k$ when a paired 2-DPC is embedded into $Q_n^k$. Compared to the other known works, our results can help $Q_n^k$ to achieve large-scale edge fault-tolerance.