Node-to-Set Disjoint Paths Problem in a Möbius Cube

Abstract

This paper proposes an algorithm that solves the node-to-set disjoint paths problem in an n-Möbius cube in polynomial-order time of n. It also gives a proof of correctness of the algorithm as well as estimating the time complexity, O(n⁴), and the maximum path length, 2n-1. A computer experiment is conducted for n=1,2,...,31 to measure the average performance of the algorithm. The results show that the average time complexity is gradually approaching to O(n³) and that the maximum path lengths cannot be attained easily over the range of n in the experiment.