A push-relabel framework for submodular function minimization and applications to parametric optimization Original Research Article

Recently, the first combinatorial strongly polynomial algorithms for submodular function minimization have been devised independently by Iwata, Fleischer, and Fujishige and by Schrijver. In this paper, we improve the running time of Schrijverʹs algorithm by designing a push-relabel framework for submodular function minimization (SFM). We also extend this algorithm to carry out parametric minimization for a strong map sequence of submodular functions in the same asymptotic running time as a single SFM. Applications include an efficient algorithm for finding a lexicographically optimal base.