A note on the minimization of symmetric and general submodular functions

Abstract

In this paper we relate the minimization problems for general submodular functions and symmetric submodular functions. We characterize the contractions and restrictions of symmetric submodular functions. The latter we show to be the same as posimodular functions. Finally, we prove the equivalence of various symmetric submodular function minimization problems and the general submodular function minimization problem. We also give a preprocessing algorithm for the general submodular function minimization problem which could lead to substantial size reduction.