Simultaneous Parametric Maximum Flow Algorithm with Vertex Balancing

Two new algorithms, SPMF and SPMF, for finding the complete chain of solutions of the selection model are presented in this paper. A special kind of residual path, called a λ-directed simple residual path, is identified to be the only kind of residual path necessary for SPMF. By augmenting the right amount of flows along the λ-directed simple residual paths, the new algorithms are monotone convergent. SPMF replaces the path-wise flow augmentation by flow-redistribution at each node, which provides a factor of ten speed-up for all the large datasets tested.