The k-ary n-cube( \(Q_n^k\) ) serves as a fundamental topology for interconnection networks in high-performance computing architectures. It has the advantages of high regularity, high fault tolerance, high bandwidth, low latency, and small network diameter. Disjoint paths can strengthen network robustness, efficiency, and reliability by offering multiple independent transmission options, and have received widespread attention. Recently, Lv et al. (J Parallel Distrib Comput 183:104761) proposed a method to construct 2n disjoint paths in \(Q_n^k\) . However, the maximum path length, which is \((n-1) \lfloor k/2 \rfloor + k - 1\) , is not optimal. Since path length directly impacts the latency and efficiency of data transmission, in this paper, we further explore the algorithm. We aim to ensure that the maximum length of disjoint paths between any two nodes in \(Q_n^k\) is at most \(n \lfloor k/2 \rfloor + 1\) . This length is optimal, given that the diameter of the network is \(n \lfloor k/2 \rfloor\) . Additionally, through simulation experiments, we compare the average path length and find that our algorithm outperforms the algorithm proposed by Lv et al. (J Parallel Distrib Comput 183:104761). We further apply the constructed disjoint paths to enhance fault-tolerant routing and data transmission.
