Constructing parallel paths between two subcubes

The authors consider a hypercube system that runs more than one job at a time, with each job allocated a subcube. They discuss the problem of migrating (relocating) a job from one subcube to another, assuming a circuit-switching hypercube network. An algorithm is presented for constructing parallel circuits between two subcubes so that the tasks of a job can be migrated simultaneously. It is shown that no matter how fragmented the hypercube is, one can always construct parallel paths between two given subcubes. Furthermore, one can always minimize the maximum length of the constructed circuits. A solution that minimizes the maximum length of the circuits will also minimize the total length. The circuits are mutually edge-disjoint and do not use any edge that has been used by other jobs. The time complexity of the algorithm is O(n²m), where n is the dimension of the hypercube system and m is the number of jobs already in the system