Node-to-Node and Node-to-Set Disjoint Paths Problems in Bicubes

Abstract

In this paper, we propose two algorithms, B-N2N and B-N2S, that solve the node-to-node and node-to-set disjoint paths problems in the bicube, respectively. We prove their correctness and that the time complexities of the B-N2N and B-N2S algorithms are O(n²) and O(n² log n), respectively, if they are applied in an n-dimensional bicube with n ≥ 5. Also, we prove that the maximum lengths of the paths generated by B-N2N and B-N2S are both n + 2. Furthermore, we have shown that the algorithms can be applied in the locally twisted cube, too, with the same performance.