Node-to-set disjoint paths problem in cross-cubes

Hypercubes are popular topologies of massive multiprocessor systems due to their super properties. Cross-cubes are significant variations of hypercubes and they have smaller diameters and higher fault-tolerant capability than hypercubes at the same dimensions. In this paper, we construct node-to-set disjoint paths of an n-dimensional cross-cube, $$C_{n}$$ , whose maximum length is limited by $$2n-3$$ . Furthermore, we propose an $$O(N \text {log}^{2}N)$$ algorithm with a view to finding node-to-set disjoint paths of $$C_{n}$$ , where N is the node number of $$C_n$$ . And we also present the simulation results for the maximal length of disjoint paths obtained by our algorithm.