A factoring algorithm for solving the problem of partitioning core networks

Double homing is effective especially for disasters; and for it to succeed on telecommunications networks, two disjoint paths are assigned between two pairs; but assigning such disjoint paths is not easy because telecommunications networks are large and complicated systems. We previously proposed a method to overcome this difficulty by partitioning a network into subnetworks that never share any common equipment. However, we had no way to check whether a network can be successfully partitioned or not, except for an approximation method. This paper proposes two new exact methods to check the partitionability of networks. One finds all the solutions, and the other performs factoring with reductions.